Graduate Diploma in Architecture_Year 01_Brief 01 by Michael Clarke

01. Learn Research document DS10

Michael Clarke

Brief_01: Learn

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Summary of Content This book documents the research undertaken for the first brief set in the first term in the first year of the Graduate Diploma in Architecture (RIBA Part II) at the University of Westminster. In addition, this book documents the process of design work utilising both analogue and digital experimentation to follow lines of enquiry established by looking at the life and workâ&#x20AC;&#x2122;s of Frei Otto and Buckminster Fuller and other influences from the initial research. This book and the brief that it answers is intended to provide a basis for the second brief of the year, the design of an arts pavilion at the Burning Man Festival in Black Rock Desert, Nevada, USA.

Michael Clarke

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Brief_01: Learn

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Page No.

Summary of Contents Brief 01: Frei Otto and Buckminster Fuller - Experimentation and learning from nature

Buckminster Fuller Ideas and Works

A brief exploration into the life and works of Buckminster Fuller from synergetics to the geodesic dome Frei Otto Ideas and Works

Looking briefly at Frei Ottoâ&#x20AC;&#x2122;s life and works including his form finding explorations and research into minimal path systems Ideals vs Irregularities

Looking to nature for examples of the perfect and the chaotic for form finding explorations following the work of Buckminster Fuller and Frei Otto

Experimentation

Looking into Frei Ottoâ&#x20AC;&#x2122;s ideas about minimal path systems and exploring these through my own analogue and digital experimental models. Learning grasshopper as a parametric tool for form finding exploration.

Michael Clarke

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Brief_01: Learn

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Buckminster Fuller Ideas and Works A brief exploration into the life and works of Buckminster Fuller from synergetics to the geodesic dome

Michael Clarke

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Frei Otto and Buckminster Fuller - Experimentation and learning from nature Brief_01: Learn

BUCKMINSTER FULLER pg. 05

Biography & Works July 1895 1914-1915 1915-1917 1917-1919 1919-1921 1922 1922-1932 1930-1932

1932-1936

1936-1938 1938-1940 1940-1950

1942-1944

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1946-1954 19491954-1959 19571959-1968

19591962-1963 1965-1967 1967-

1968-1970

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1972-1983

1972 1972-1974 1973

1974 1974-1983

1975-1983

Buckminster Fuller was born in Milton, Massachusetts on the 12th July Apprentice machine ¿tter, Richards, Atkinson, & Haserick, Boston, importers of cotton mill machinery. Various apprentice jobs, Armour & Co, New York City. Ensign U.S.N.R. to Lieutenant U.S.N. United States Navy, World War I. Assistant Export Manager, Armour & Company. National Account Sales Manager, Kelly - Spring¿eld Truck Company. President, Stockade Building System, 240 Building Operations. Editor, Publisher, Shelter magazine. Assistant to Director of Research, Pierce Foundation & American Radiator Standard Manufacturing Company; produced mass-production kitchen and bathroom back to back. Director and Chief Engineer, Dymaxion Corporation; Bridgeport, Connecticut; produced 3 Dymaxion Cars. Assistant to Director, Research and Development, Phelps Dodge Corporation. Science and Technology Consultant, Fortune magazine. Vice President, Chief Engineer, Dymaxion Company, Inc., Delaware, Associated with Butler Manufacturing Company. Produced Dymaxion Dwelling Unit. Chief Mechanical Engineer, US Board of Economic Warfare, World War II. Special Assistant to Deputy Director, US Foreign Economic Adminstration. Chairman of Board, Chief Engineer, Dymaxion Dwelling Machine Corporation (later) Fuller Houses, Beech Aircraft Company; Wichita, Kansas. Chairman, Board of Trustees, Fuller Research Foundation, Wichita, Kansas. President, Geodesics, Inc.; Forest Hills, New York. President, Synergetics, Inc.; Raleigh, North Carolina. President, Plydomes, Inc.; Des Moines, Iowa. Research Professor, Design Science Exploration, Director of Inventory of World Resources, Human Trends and Needs. Founder, Director of World Game. Director of Design Science Decade of International Union of Architects, Southern Illinois University. Chairman of the Board, Tetrahelix Corporation; Hamilton, Ohio. Charles Eliot Norton Professor of Poetry, Harvard University. The Architect of U.S. Pavilion at Expo ‘67 Montreal World’s Fair. President, Triton Foundation. Architect in production of the Tetrahedronal Floating City for US Department of Housing and Urban Development. Architect in collaboration with T. C. Howard of Synergetics, Inc., of the Tri-Centennial Pavilion of South Carolina at Green¿eld, South Carolina. University Professor, Southern Illinois University. Architect, Samuel Beckett Theater, St. Peters College, Oxford University; Oxford, England. Architect, geodesic auditorium, Kfar Mena Chem Kibbutz, Israel. World Game seminars at Yale University and New York Studio School. Chief Architect, Old Man River Project (Environmental Domed City), East St. Louis, Illinois. Architect, Project Toronto, Toronto, Canada. Architect, Religious Center at Southern Illinois University, Edwardsville, Illinois. Architect, design of St. Peters Theatre, London, England. World Fellow in Residence for the Consortium of the University of Pennsylvania, Bryan Mawr, Haverford and Swarthmore Colleges and the University City Science Center, Philadelphia, Pennsylvania. Editor-at-Large, World Magazine; Consultant, DESIGN SCIENCE INSTITUTE. Distinguished University Professor, Southern Illinois University, Carbondale and Edwardsville, Illinois. Chief Architect, Completion of the Design for the International Airports at New Delhi, Bombay, and Madras, India. Author of Synergetics, Explorations in the Geometry of Thinking (published 1975). Consultant, Design Science Institute. Consultant, Design Science Institute. Consultant to Architects Team 3 (designing $200 million Penang Urban Center), Penang, Malaysia, becoming Team 3 International in 1981 Appointed University Professor Emeritus, Southern Illinois University, Carbondale and Edwardsville, Illinois.

1975-1983 1975

1975-1980 1975-1977 1976

1977

1978 1978-1983 1979-1983 1979-1983 1979

1980 1981-1983 1981 1982

July 1983

Appointed University Professor Emeritus, University of Pennsylvania, Philadelphia, Pennsylvania. Member of Advisory Council on International Programs, Bryan Mawr College, Bryan Mawr, Pennsylvania. Member of Advisory Committee, Windworks, Mukwonago, Wisconsin. Tutor in Design Science, International Community College, Los Angeles, California. International President, World Society for Ekistics. Conceived and designed Synergetics exhibit for the opening of the Smithsonian / Cooper Hewitt Museum of Design. Author, artist and designer of a limited edition lithograph ‘Tetrascroll’. Author and designer of a limited edition of silk-screens Synergetics Poster Series. Conceived and designed a limited edition of metal sculpture Jitterbug. Author of And it Came to Pass, Not to Stay. Designed and developed two prototype geodesic domes “Pinecone Dome” and “Fly’s Eye Dome”. Lecturer, Far Eastern tour sponsored by the U.S. State Department/United States Information Agency. Scholar in Residence, University of Massachusetts, Amherst, Massachusetts. Senior partner, Fuller & Sadao PC, Long Island City, New York. Chairman of the Board, R. Buckminster Fuller Sadao & Zung Architects, Inc., Cleveland, Ohio. Senior partner, Buckminster Fuller Associates, London, England. Author, Synergetics 2, Further Explorations in the Geometry of Thinking, published by Macmillan. Author, R. Buckminster Fuller On Education, published by University of Massachusetts Press. Author, Critical Path, to be published winter 1980-81 by St. Martin’s Press. Chairman, Fuller-Patterson Corporation and Buckminster Fuller Research and Development Park. Author, Grunch of Giants, to be published winter 1982-3 by St. Martin’s Press. Designed and developed tensional Dymaxion Hanging Bookshelf. Designed and developed deresonated Tensegrity dome. Author, Inventions (working title) to be published 1983 by St. Martin’s Press. Designed and developed steel strap model of spherical to planar triangular transformation. Designed BigMap, basketball-court-sized Dymaxion projection displayed to U.S. Congress. Bucky and Anne died within thirty-six hours of each other, one week before their sixty-sixth anniversary, Bucky on July 1st 1983, Anne on July 3rd 1983.

Michael Clarke

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Brief_01: Learn

The Impact of Fuller’s Early Life Fuller’s life was not easy and his outlook in later life and a commitment to his philosophies may have sprang from this. ‘His philosophy is centered around the human potential to overcome whatever “reÀex conditioning” might have entrapped our humanity in counterproductive scenarios.’ Fuller was often considered eccentric and an outsider, especially in the world of academia. ‘Although the family had a four-generation tradition of sending its sons to Harvard, Fuller was too much the wild romantic to settle in and was expelled for treating an entire New York dance troupe to champagne on his own tab. The family sentenced him to hard labo[u]r in a Canadian cotton mill, where he sobered up quite a bit, but he still didn’t like Harvard upon giving it a second try and was again expelled. He later returned to Harvard as the Charles Eliot Norton Professor of Poetry (1962).”’ In 1917 Fuller entered the Navy obtaining a command and later went on to the Annopolis Naval Academy in 1918. ‘A few years after his honorable discharge from the Naval Academy, Fuller attempted to make money using his father-in-law’s invention, a morterless brick building system, but failed in this enterprise (1926). This failure, which led to joblessness in Chicago, coupled with the trauma of losing his ¿rst child Alexandra to prolonged illness in 1922, pushed Fuller to the brink in 1927. He considered suicide but, as he put it, resolved to commit ‘egocide’ instead, and turn the rest of his life into an experiment about what kind of positive difference the ‘little individual’ could make on the world stage. He called himself ‘Guinea Pig B’ (B for Bucky) and resolved to do his own thinking, starting over from scratch. Hugh Kenner likens this to Descartes’ resolve to shut himself in a room until he’d discerned God’s truth -- a kind of archetypal commitment to a solitary journey.’ This great experiment governed much of Fuller’s work. All of Fuller’s work sought to make the biggest contribution to the world as a whole. There are many articles pointing out that Fuller never intended to design anything speci¿c, instead he approached problems that could be solved. He labelled many of his discoveries and inventions under philosophies such as Synergetics, Design Science and Dymaxion all summarised over the next few pages. What he later called the dymaxion chrono¿le was his extensive documentation of his life including all his works, drawings, patents and thoughts. ‘The Chrono¿le was comprehensive to the point of being unintelligible, but accurately captures the spirit of this great intellectual omnivore’s attitude towards life. He was an inventor, but not of single objects: his whole life was devoted to the creation of a new world.’ Although not always accepted Fuller de¿nitely had an impact on some if not the whole of humanity he sought. It is only now that much of his work is being re-examined. His thoughts for economising materials and futuristic discourses for an entire way of living that sought to rationalise and minimise energy systems are certainly relevant today. Although many of his revolutionary projects became one off prototypes some can be seen all over the world such as the geodesic dome. He is regarded as one of the last Utopian thinkers and a great modern day visionary compared by some even to Leonardo Da Vinci in his passion for engineering, design, philosophy, science and the arts.

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Championing ‘Bucky’

Critics of Fuller and his character

The images on this page show some examples of Buckminster Fuller’s impact on the world today.

Fuller’s role as an outsider led to many criticising his works, not just championing it. He did little to appease his critics however and,

The Buckminster Fuller Institute’s ‘Buckminster Fuller Challenge’ competition. The Institute tries to bring together ideas from across varying disciplines whilst maintaining a record of Buckminster Fuller’s life and works. The competition rewards solutions from across the globe to social, political and environmental problems trying to build on the legacy left by Buckminster Fuller.

‘devoted his life to becoming, in his own words, “the world’s most successful failure”.’ The following extract taken from Kirby Urner’s online post ‘R. Buckminster Fuller: A 20th Century Philosopher’ accounts for some of Fuller’s chief failings in relation to his peer groups:

A molecule named Buckminsterfullerene. Discovered in 1985, the molecule, an allotrope of carbon in much the same way as graphite or diamond, was named after Buckminster Fuller when the structure was found to resemble Fuller’s geodesic dome. Other fullerenes have since been found although C60 is the most common. This allotrope is the principle molecule found in carbon nanotubes.

‘It was over this concept of ‘tensegrity’ that early divisions over the issue of Fuller’s character and integrity came to the foreground. Ken Snelson, a star pupil at Black Mountain College (1948), at ¿rst enchanted by Bucky’s spell, became highly disillusioned when it appeared that Fuller planned to abscond with the “tensegrity” idea without properly crediting his student.

Images from Drop City. Drop city was the ¿rst commune in the world set up in the desert of Colorado. Fuller’s geodesic dome was seen as symbolising a new way of living. These structures resembling the domes were made from a mixture of found materials including cloth, timber and scrap metal. The commune was set up to provide an open community able to breed ideas and form a platform for ‘drop in’ artworks in an area free from the pressures of everyday life. The philosophy of the commune and the limit on resources in the structures was very akin to Buckminster Fuller’s ideal and the original founders along with 6 additional people at the commune were presented the Buckminster Fuller Dymaxion award.

Fuller’s reputation for egomania and improperly seizing upon others’ ideas as his own may be traced to this Fuller-Snelson split, and led many to question whether the geodesic dome, widely credited to Fuller (who took out a number of patents around the idea) was another case in point. Walter Bauresfeld had hit on the same strategy in 1922, for use in constructing planetaria. Alexander Graham Bell had also made extensive use of the octet truss circa 1907, another one of Fuller’s key concepts (also patented). Fuller’s own archives, maintained since his death in 1983 by the Buckminster Fuller Institute (BFI) and his estate (EBF), details his side of the story and he seems to have died with a clear conscience regarding these matters -- realizing they would remain bones of contention. His collaboration with Werner Erhard (late 1970s on), a self-styled “est Trainer” who shared his home-grown philosophy of the mind using a hard-hitting seminar format, marked another chapter fraught with controversy. Fuller, as per usual, took pains to fully document the relationship for his Chrono¿le (an exhaustive record of the Guinea Pig B experiment), making it especially clear that Erhard’s group in no way ever funded or underwrote any of his activities. On the contrary, Fuller wanted to be seen as giving Erhard, many years his junior, a welcome boost from an independent platform. Fuller’s contribution has for the most part not penetrated to academia’s required reading syllabi within any department as of this writing (May, 1998), in part because Fuller himself remained largely aloof to speciation within the university system, and therefore was never embraced by any professional peer group, except by architects.’

Michael Clarke

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Brief_01: Learn

Dymaxion The word: The dymaxion phrase came about from Waldo Warren, an advertising expert, who was working on a brand for Fuller to display his ¿rst architectural model under, the dymaxion house. It came from an analysis of the words and language that Fuller commonly used. Fuller used the phrase for a whole series of works shown on this page. In simplistic terms it means doing more with less, much like Fuller’s ideas on synergetics. The dymaxion ideas, models and prototypes formed Fuller’s portfolio of ideas to rationalise living patterns and change the way society viewed objects such as the car or the bathroom.

The car: The dymaxion car was a streamlined lightweight three wheeler. It weighed around only 1000lbs and was approximately 20ft long. It had a ford engine mounted in the rear with the single rear wheel being responsible for the steering. The car was able to hold ten passengers and reach speeds of up to 120mph and 30mpg. However only three were ever made and there were problems. the single wheel at the rear responsible for the steering made it dif¿cult to control, particularly in crosswinds.

The map: Buckminster Fuller experimented with the world map for several decades coming up with what he labelled as the dymaxion map in 1954. In most Àat projections of the globe there are distortions where some landmasses are represented disproportionately to their actual size such as Greenland, sometimes shown up to three times larger than its actual size. Fuller viewed these maps as just one of the many things in popular culture and education impeding a common future: ‘Instead of serving as “a precise means for seeing the world from the dynamic, cosmic and comprehensive viewpoint,” the maps we use still cause humanity to “appear inherently disassociated, remote, self-interestedly preoccupied with the political concept of its got to be you or me; there is not enough for both.”’* Fuller’s projection is the most realistic showing almost no distortion in the landmasses. By also representing it as a singular connected landmass with one ocean he also hoped to limit the economic and political boundaries.

The house: There were two iterations of the Dymaxion house although only one was ever built and limited to a one-off instead of the mass produced house that could ¿t anywhere that it was designed to be. The initial model and designs were for a house hung around a central column with the supporting cables on the exterior. The house was designed to cost no more than a car and be able to be transported anywhere in the world in its own metal tube. The Buckminster Fuller Institute describes the house, ‘Bucky designed a home that was heated and cooled by natural means, that made its own power, was earthquake and storm-proof, and made of permanent, engineered materials that required no periodic painting, reroo¿ng, or other maintenance. You could easily change the Àoor plan as required - squeezing the bedrooms to make the living room bigger for a party, for instance. Downdraft ventilation drew dust to the baseboards and through ¿lters, greatly reducing the need to vacuum and dust. O-Volving Shelves required no bending; rotating closets brought the clothes to you. The Dymaxion House was to be leased, or priced like an automobile, to be paid off in ¿ve years.’ The original version of the house was never built to Fuller’s original speci¿cation although ‘two versions were built’. May criticised the use of aluminium being a high energy material although Fuller argued that aluminium kept down the weight, it was extremely strong and durable outweighing initial cost and energy in production. Many people disliked the overall aesthetic of the house as well. The original was designed in the 1920s with versions not being built until 1945. In 1946 Fuller redesigned the house with a round Àoor plan and the structure being hidden on the interior. The same principles applied and the built house (also called the wichita house) survived a nearby tornado in 1964. Perhaps most impressive is the entire weight of the house was only around 3000lbs. Every part of the house was designed to Bucky’s exacting standards with the dymaxion bathroom one of the most impressive parts however Fuller felt he could improve it and never let it go into production.

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The dymaxion car (above) was not Fuller’s only vehicle. He also developed a new rowing boat with two blades in the water and an elevated seat suspended between. His vehicles focused on as aerodynamic solution as possible using aas few materials.

Fuller’s designs incorporated every last detail. His ideas for the dymaxion house were supposed to spark a whole new way of living and he carried this through into the bathroom design. Also under the dymaxion brand this was a modular design with copper ¿ttings inside.

Above is Fuller’s design for the original dymaxion house with the support structure on the outside. The later iteration that was ready for production before Fuller stopped it is shown to the left. This was the only built dymaxion house also known as Wichita House.

Michael Clarke

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Brief_01: Learn

Vector Equilibrium Fuller’s work in geometry pushed radical new directions. Many of his explorations with form he devised new terms for describing the phenomena he came across. Although often formed from simple shapes Fuller worked with very complex geometries. Every exploration looked at ¿nding a simple rational, looking at the minimum way of achieving a goal, the maximum geometries that could tesellate and minimum energy systems. Particularly important in this exploration was his work with ‘Vector Equilibriums’. Fuller’s work in this ¿eld derived from a fascination with the packing of spheres in space. His vector systems were generated from drawing lines between the centres of the spheres. ‘Unlike the geometers before him, Fuller did not start with a point, then a line, then a plane to which he then added dimension. He started in the center of the sphere and out in all directions. The lines or vectors represented energy, direction and time.’# Limiting the explanation purely to the vector lines for now we can start by looking at the symmetry involved in a plane. The hexagon is the only shape where the edge length is equal to the distance from the vertices to the centre (Fig. #). In the same vein, the only three-dimensional form (polyhedra) where every edge length is equal to the distance from each vertex to the centre is the cuboctahedron (Fig. #). It is also evident that 4 hexagons can be found in this shape (Fig. #). Going back to the spheres Fuller found that the maximum number of spheres that can be formed around a single sphere is 12. This is illustrated in the ¿rst image (Fig. #). Bounding the spheres is the cuboctahedron which bounds the centre lines of the spheres. The sculpture shows off the de¿ning principles of Fuller’s vector equilibrium.

Tensegrity Structures

‘“The word ‘tensegrity’ is an invention: a contraction of ‘tensional integrity.’ Tensegrity describes a structural-relationship principle in which structural shape is guarenteed by the ¿nitely closed, comprehensively continuous, tensional behaviors of the system and not by the discontinuous and exclusively local compressional member behaviors. Tensegrity provides the ability to yield increasingly without ultimately breaking or coming asunder” - Richard Buckminster Fuller (exerpt from Synergetics, p. 372.)’ This basically means that a tensegrity system is a zero energy system. Each compression member is isolated from every other separated by a net of tension members. Another word for this system is Àoating compression used mainly by Kenneth Snelson, a former student of Buckminster Fuller’s who we came across earlier when Fuller refused to credit his student for his work on tensegrity structures.

Tensegrity can be likened very simply to a balloon.THe outside surface of the balloon is in constant tension whereas the air inside is in compression. any external force is distributed across the entire system# Tensegrity was a key idea in FUller’s Synergetics. The idea of tension vs compression both acting together was one of the many opposites that co-exist. Synergy is explained fuller in later pages. The picture to the top is of a tensegrity dome. Tensegrity structures are very light and for their comparitive mass extremely rigid due to the lack of any bending moment in any of the members. Key examples of tensegrity are the dome pictured top, the Skylon tower in 1951 far left, and later structures such as the Needle Tower, second from left and a reusable easy to deploy structure on the right.

Top: Fuller’s diagram for vector equilibrium. It shows the make up of the cuboctohedron from 8 tetrahedrons and 6 half octahedrons. Bottom left: The regular hexagon is the only polygon where the edge lengths are also equal to the length from each vertex or point to the polygons centre. Bottom middle: A diagram highlighting the hexagons found in a cuboctahedron. Bottom right: A sculpture commissioned by Fuller for the maximum number of spheres packed around a central sphere. The structure surrounding the spheres is the cuboctohedron.

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The tensegrity sphere. The whole structure is in a state of equilibrium with the members in compression producing an equilibrium with the members in tension. None of the compression members in the sphere touch each other. The same principles can be applied to other tensegrity structures.

Left top: A model of the ‘jitterbug’ in the open position. Left bottom: The same model fully closed as an octohedron. Right: Another sculpture commissioned by Fuller called a ‘complex of jitterbugs’.

Michael Clarke

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Brief_01: Learn

A Holistic Approach

Design Science Planning

Many of Buckmister Fuller’s philosophies looked at approaching problems with a holistic approach aiming to encompass all of humanity. He developed theories for identifying problems and solutions and looked at many systems in nature, including humanity, as being interconnected. By taking a step back and looking at the larger image he was able to de¿ne his work to a scale applicable across the world in his own view.

Inventor alternativ

Choose problem situation

De¿ne problems

De¿ne preferred state

Describe present state

Develop evaluatio criteria

Synergetics

Design Science

Synergetics was one of Fuller’s philosophies that pervaded much of his work. It is also the title of a book Fuller wrote on the same subject.

Design Science follows Fuller’s thoughts on synergetics as a holistic approach. ‘“The function of what I call design science is to solve problems by introducing into the environment new artifacts, the availability of which will induce their spontaneous employment by humans and thus, coincidentally, cause humans to abandon their previous problem-producing behaviors and devices. For example, when humans have a vital need to cross the roaring rapids of a river, as a design scientist I would design them a bridge, causing them, I am sure, to abandon spontaneously and forever the risking of their lives by trying to swim to the other shore.”

‘Synergetics, short for synergetic-energetic geometry, systematizes its concepts around a core polarity variously labeled as: synergy vs. energy growth vs. decay tension vs. compression syntropy vs. entropy gravity vs. radiation. These paired tendencies ‘always and only co-occur’ and do not come across as moral catagories in any primary sense, nor should Synergetics be regarded as a theological work, despite its transcendentalist proclivities. The ethical direction in synergetics is towards “omnieconomical design” with nature’s “technologies” setting the standard. Our humanly contrived inventions work

nature’s ideals and as we become more adept at using basic principles to best advantage, our designs accomplish more with less physical time/energy expenditures -- a long term trend Fuller labeled “ephemeralization” ‘ to approach

Although often talked about in relation to geometry, synergetics was about entire systems, ‘101.01 Synergy means behaviour of whole systems unpredicted by the behaviour of their parts taken separately. 102.00 Synergy means behaviour of integral, aggregate, whole systems unpredicted by behaviours of any of their components or subassemblies of their components taken separately from the whole. 962.40 Synergetic geometry embraces all the qualities of experience, all aspects of being.’

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- R. Buckminster Fuller, from Cosmography Design Science is a problem solving approach which entails a rigorous, systematic study of the deliberate ordering of the components in our Universe. Fuller believed that this study needs to be comprehensive in order to gain a global perspective when pursuing solutions to problems humanity is facing.’

Process ry ves

Design preferred system

Develop artifacts

Develop implementation strategies

Document process

Communicate plan

Initiate larger planning process

p on

Triton City ‘Buckminster Fuller designed this tetrahedronal Àoating city for Tokyo bay in the 1960’s. He wrote: “Three-quarters of our planet Earth is covered with water, most of which may Àoat organic cities...Floating cities pay no rent to landlords. They are situated on the water, which they desalinate and recirculate in many useful and nonpolluting ways. They are ships with all an ocean ship’s technical autonomy, but they are also ships that will always be anchored. They don’t have to go anywhere. Their shape and its human-life accommodations are not compromised, as must be the shape of the living quarters of ships whose hull shapes are constructed so that they may slip, ¿shlike, at high speed through the water and high seas with maximum economy...Floating cities are designed with the most buoyantly stable conformation of deep-sea bell-buoys. Their omnisurface-terraced, slop-faced, tetrahedronal structuring is employed to avoid the lethal threat of precipitous falls by humans from vertically sheer high-rising buildings...The tetrahedron has the most surface with the least volume of all polyhedra. As such, it provides the most possible ‘outside’ living. Its sloping external surface is adequate for all its occupants to enjoy their own private, outside, tiered-terracing, garden homes. These are most economically serviced from the common, omni-nearest-possible center of volume of all polyhedra...When suitable, the Àoating cities are equipped with ‘alongside’ or interiorly lagooned marinas for the safe mooring of the sail- and powerboats of the Àoating-city occupants. When moored in protected waters, the Àoating cities may be connected to the land by bridgeways.

city for anchorage just offshore in Chesapeake Bay, adjacent to Baltimore’s waterfront. At this time President Lyndon Johnson’s Democratic party went out of power. President Johnson took the model with him and installed it in his LBJ Texas library. The city of Baltimore’s politicians went out of favor with the Nixon administration, and the whole project languished.”’ Triton City was developed from a tetrahedron, the largest possible surface area from a volume in order to maximise access to natural light and balcony space for all it’s residents. The inside was hollowed out to provide communal, civic and leisure space for the citiy’s inhabitants. Many of the concepts from the city are relevant in planning and design decisions for residential developments today.

In 1966 my Japanese patron died, and the United States Department of Housing and Urban Development commissioned me to carry out full design and economic analysis of the Àoating tetrahedronal city for potential U.S.A use. With my associates I completed the design and study as well as a scaled-down model. The studies showed that the fabricating and operating costs were such that a Àoating city could sustain a high standard of living, yet be economically occupiable at a rental so low as to be just above that rated as the ‘poverty’ level by HUD authorities. The secretary of HUD sent the drawings, engineering studies, and economic analysis to the Secretary of the Navy, who ordered the Navy’s Bureau of Ships to analyze the project for its ‘water-worthiness.’ stability, and organic capability. The Bureau of Ships veri¿ed all our calculations and found the design to be practical and ‘waterworthy.’ The Secretary of the Navy then sent the project to the US Navy’s Bureau of Yards and Docks, where its fabrication and assembly procedures and cost were analyzed on a basis of the ‘Àoating city’ being built in a shipyard as are aircraft carriers and other vessels. The cost analysis of the Navy Department came out within 10 percent of our cost - which bore out its occupiability at rental just above the poverty class. ``At this point the city of Baltimore became interested in acquiring the ¿rst such Àoating

Michael Clarke

pg. 14

Brief_01: Learn

The Geodesic Dome Fuller’s work often looked at ¿nding the maximum amount of space that could be formed with the minimal amount of materials. This tied in with his ideas of design science and synergetics trying to make the most of the earth’s resources for the bene¿t of humanity. With his work in geometry and knowledge of structures Fuller knew that the triangle was inherently stronger than the square which would collapse under any pressure. These ideas led to what has been termed as Fuller’s most famous discovery, the geodesic dome. ‘A geodesic dome is a structure comprised of a complex network of triangles that form a roughly spherical surface. The more complex the network of triangles, the more closely the dome approximates the shape of a true sphere. “By using triangles of various sizes, a sphere can be symmetrically divided by thirty-one great circles. A great circle is the largest circle that can be drawn around a sphere, like the lines of latitude or longitude around the earth. Each of these lines divide the sphere into two halves, hence the term geodesic, which is from the Latin meaning “earth dividing”.’ Fuller patented his idea at the US Patent of¿ce in 1951 being approved in 1954, however, it didn’t become large built structures until quite a few years later. The dome received many plaudits worldwide once it began to appear. Fuller’s ¿rst worldwide acceptance of his idea was after presenting a model of his geodesic dome at the Milan triennial in 1954. ‘The theme for 1954 was Life Between Artifact and Nature: Design and the Environmental Challenge which ¿t in perfectly with Bucky’s work. Bucky had begun efforts towards the development of a Comprehensive Anticipatory Design Science which he de¿ned as, “the effective application of the principles of science to the conscious design of our total environment in order to help make the Earth’s ¿nite resources meet the needs of all humanity without disrupting the ecological processes of the planet.” The cardboard shelter that was part of his exhibit could be easily shipped and assembled with the directions printed right on the cardboard. The 42-foot paperboard Geodesic was installed in old Sforza garden in Milan and came away with the highest award, the Gran Premio.’ The US Army also recognised the potential of Fuller’s design and had already begun to look at domes as a cheap and speedy solution to soldiers housing abroad. In 1964 Fuller received the commission to design the US pavilion for the 1967 Montreal Expo. ‘The 250-foot diameter 3/4 geodesic sphere was constructed of steel and skinned with Plexiglas. Opened in April, 1967, this “skybreak bubble,” called “Buckminster Cathedral” by Peter Ustinov, drew record-breaking crowds of more than ¿fty million in its ¿rst six months and in 1968 was awarded the ¿rst Architectural Design Award by the American Institute of Architects.’ Fuller developed two further iterations of his geodesic dome, the ¿rst was for an improved laminar geodesic dome which he submitted to the patent of¿ce in 1960, the second was a monohex or Ày’s eye dome that was submitted the following year. The Ày’s eye is 5/8 of a geodesic sphere and was intended as another housing solution. Large circular openings served as windows or doors and places for solar collectors or turbines etc. The structure itself is made from ¿breglass. Both these later domes gained patents in 1965.

Fuller’s largest geodesic structure, the US pavilion at the Montreal Expo. Fuller was responsible for the dome on the outside whilst

pg. 15

The Flyâ&#x20AC;&#x2122;s Eye Dome

The geodesic dome as a solution to extreme climates. It is the structure most commonly used for biospheres such as the eden project in Cornwall. The versatility of the dome and is highlighted by the dome at the antartica base camp (left).

Michael Clarke

pg. 16

Brief_01: Learn

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Frei Otto Ideas and Works Looking brieÀy at Frei Otto’s life and works including his form ¿nding explorations and research into minimal path systems

Michael Clarke

pg. 18

Brief_01: Learn

FREI OTTO pg. 19

Biography 1925 1940

1943

1943/45 1945/47 1948/52 1950

1952 1953 1954 1957 1957 1958 1960 1961 1961/62 1962 -

1964

1965 1968 1971 1973 1975

1987

Works Born in Siegmar, Saxony, Germany He spent his adolescence in Berlin and worked during the school holidays as a stone mason. He also learnt to pilot gliders. He graduated from the Schadow-Schule in Berlin-Zehlendorf. He began studying architecture at the Technische Universität in Berlin He served his military service as a pilot in an air ¿ghter squadron He was taken prisoner near Chartres, in France and became the prison camp architect He completed his architectural studies at the Technische Universität in Berlin, taught by Professors H. Freese, H. Bickenbach, G. Jobst, and winning a scholarship to study at the “Studienstiftung des Deutschen Volkes” Study tour to the United States to see the works of Wright, Mendelson, Saarinen, Mies van der Rohe, Neutra and Eames. He studied sociology and town planning for two months at the University of Virginia, at Charlottesville He graduated and set up his own practice in Berlin He presented his degree thesis “Das Hängende Dach” (Suspended roofs) He was awarded a prize for his degree thesis He set up the Entwicklungsstätte für den Leichtbau Visiting professor at the University of Washington, St. Louis for a seminar on lightweight structures He held a series of lessons at the Hochschule für Gestaltung, in Ulm He was appointed visiting professor at Yale University in New Haven He became a member of the Biologie und Bauen research group He was appointed assistant to P. Poelzig at the Technische Universität in Berlin He held a seminar on minimal structures at the Technische Universität in Berlin. Visiting professor at the University of California, in Berkeley, at MIT and at Harvard University in Cambridge. He held a seminar at the Universidad del Zulia in Maracaibo Visiting professor at the Technische Universität in Stuttgart. He held a correspondence seminar at the Universidad del Zulia in Maracaibo. He set up the Institut für Leichte Flächentragwerke (institute for lightweight structures) at the Technische Universität in Stuttgart. He was appointed as professor at the Technische Universität in Stuttgart He was made an honorary member of the American Institute of Architects He was appointed professor of architecture at the International Summer Academy for visual arts, in Salzburg. He was awarded an honorary degree by the University of Washington, St. Louis. He was awarded an honorary degree in Science at the University of Bath 1978 - He was elected honorary member of the Institute of Structural Engineers He was made an academician of the International Academy of Architecture

1955 1957 1963 1965 1965 1965 1967

1968 1968/69 1969 1969/70 1970 1970/71 1971 1972 1972/73 1973 1973/74 1974

1978 1979 1980 1980/85 1981 1982 1985 1985/86 1988 1992 1997 1998 2000

Bandstand at the Federal Garden Exhibition, Kassel (Germany) Built in 1955. Shelter Pavilion at the Federal Garden Exhibition, Cologne (Germany) Built in 1957. Enlargement and roo¿ng of the open-air theatre at Wunsiedel (Germany). Built in 1967/68. Roo¿ng for the Masque de Fer open-air theatre in Cannes (France). Built in 1965. Pavilion for the Federal Republic of Germany for the Expo ‘67 in Montreal (Canada). Built in 1966/67. Project for temporary roo¿ng for the Medical Academy in Ulm (Germany). Architect’s house and studio in Warmbronn, near Stuttgart, Germany; project for the Indian Pavilion at Expo ‘70 in Osaka, Japan; roo¿ng of the open-air theatre in the ruins of an abbey at Bad Herzfeld, Germany; Institut für Leichte Flächentragwerke (institute for lightweight structures) building in Stuttgart Vaihingen, Germany; roo¿ng for the sports facilities for the 1972 Olympic Games, at the Olimpiapark in Munich, Germany. He was awarded the Berlin Art Prize and the Prix Perret by the International Union of Architects Roo¿ng of the ice rink at ConÀans-Ste-Honorine. Hotel and conference centre at the Mecca (Saudi Arabia). Project for the Kuwait Sports Center for the PanArabian Games in 1974, Kuwait; project for a foot bridge in Berlin - Wilmersdorf, Germany. Roo¿ng at the Federal Garden Exhibition in Cologne, Germany. Project for a “multimedia” roof for the Hoechst Stadium, Germany; roo¿ng for the open-air swimming pool in Regensburg, West Germany. project for a town in the Arctic. Stuttgart Bonatzpreis for his work at the Institut für Leichte Flächentragwerke; Kolner Kunstpreis. Project for desert sunshade structures; honorary Plastics Use in Building prize awarded by the Club of Plastics Use. Project for a cultural and shopping centre in Abidjan, Ivory Coast. Project for the Sarabhai Tent at Ahmadabad; project for the birdhouse in Ludwigsburg. Roo¿ng of the multifunctional hall at the Federal Garden Exhibition in 1975 at Mannheim, Germany; protective roo¿ng for the historical carousel in the grounds of the Smithsonian Institute in Washington, United States. Project for a Cooling Tower; project for spa baths at the old Police Station in Baden-Baden; project for the roof over the stage in the open-air theatre in Scarborough in England; project for roo¿ng of a tennis court in Hammamet, near Tunis, Tunisia; Thomas Jefferson Medal and Prize, University of Virginia. Hugo-Haring Prize. Deutscher Holzbaupreis. Aga Khan Award for Architecture (Lahore). Diplomatic Club of the diplomatic corps in Riyadh (Saudi Arabia). Sports Hall for the King Abdulaziz University, Jeddah. Grosser BDA Preis, Biberach. New roof for the Wilkhahn production department, in Bad Münder (Germany). Prototypes for housing at Hooke Park, Dorset (Great Britain). Temporary tent used for the Pope’s visit to Bamberg. Competition for the German pavilion at Expo ‘92. Wolf Prize in Architecture, Israel Central station, Stuttgart; Aga Khan Award for Architecture Special Prize of the VII International Biennial for Architecture, Buenos Aires.

Michael Clarke

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Brief_01: Learn

From Soap Film to Structure_Minimal Surfaces Minimal surface Tension nets pneumatic structures

pg. 21

Michael Clarke

pg. 22

Brief_01: Learn

Frei Otto’s Path Networks A lot of Frei Otto’s experiments focused on connections. He, ‘distinguishes empirically three scalar levels of path networks, each with its own typical con¿guration: settlement path networks, territory path networks and long-distance path networks. All start as forking systems that eventually close into continuous networks. In tandem, Otto distinguishes three fundamental types of con¿guration: direct path networks, minimal path networks and minimising detour networks’1 ‘Optimised Path Systems’ Imagining a road network Frei Otto set up an analogue experiment involving woolen threads. First pins were placed in a board around the circumference of a circle representing every possible destination. A tight thread was then connected from every pin to every other pin representing the journey. The result is a highly geometric shape and very symmetrical with far more routes than necessary if one was to plan a road network. The model simply represents a map of every possible route to every destination (¿g. 1). This is also representative of a direct path network. What Otto then did was to lengthen every thread by approximately 8% (¿g. 2). This maintains all the routes but now taking into account an average ‘detour’ across each route. Although no longer geometrically ordered there is still the surplus of roads and a messy incoherent network. The whole network of threads is then dipped in water. By allowing the additional thread length the threads begin to adhere in places bringing an organisational system to the network. In places many threads will stick together whereas in others single threads are left (¿g. 3). It sets up a hierarchy of routes. This system allows the calculation of an optimal path for any given ‘length’ of detour. Although for each length every outcome or solution will be unique patterns can be seen in the way the threads are grouped or organised. Other architects and engineers have studied Frei Otto’s system. Lars Spuybroek, director of NOX has drawn on Frei Otto’s work in the development of a ‘wet grid’. Something he sees as softer and more adaptable, accounting for time and therefore stronger than the top down structured grid commonly in use in rationalised architecture.2

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Michael Clarke

pg. 24

Brief_01: Learn

pg. 25

Ideals vs Irregularities Looking to nature for examples of the perfect and the chaotic for form 多nding explorations following the work of Buckminster Fuller and Frei Otto

Michael Clarke

pg. 26

Brief_01: Learn

Frei Otto vs. Buckminster Fuller Although not actually opposing the work of one another or even differing in opinion often, the title is intended to represent a difference of opinion that will serve as the focus for this stage of research and experimentation. Both men, as architects, engineers and even philosophers drew inÀuence for their work from nature. Both have also remarked on the ef¿ciencies that can be found in nature and that lessons can be learnt by studying natural systems. However, Fuller believed that nature is perfect in every way and that everything we do should aim to replicate the world around us. As I have noted, in his work on synergetics, there is a trend in human work labelled by Fuller as ‘ephemeralisation’ as humans try to match nature’s ideals. Fuller also stated that human’s were a part of nature and also subject to it’s laws and guidances.

Phyllotaxis

‘Nature is trying very hard to make us succeed, but nature does not depend on us. We are not the only experiment.’

Self-organising s

Perhaps the most telling quote from Fuller is the following in which he categorically states the perfect ideal that nature sets us:

‘The opposite of nature is impossible’ Frei Otto, as I have said, did not disagree that lessons could be learnt from nature only his philosophies debated the extent to which we should try to copy. Many of Otto’s analogue experiments draw from the most ef¿cient paths and surfaces created by soap ¿lms for example. Otto also looked at the structural properties of bamboo and spiders webs as well as the lightweight construction found in things such as bird skulls. All the time he was interested in the forms that are created, the material properties and the structural stabilities. However Otto also noted that not everything in nature is perfectly laid out.

“Irregularity is important not only in biology but also in technology, and is a field that has not been researched enough’’ We should not always look to fully replicate nature and that discoveries can be born from things that are outside of the system. Although not a focus of Otto’s research I am looking to take this idea of imperfections, irregularities and redundancies in nature and natural systems in contrast with the perfections cited by both architects as a starting point for my own research and experimentation.

IDEALS Logarithmic spirals and the golden ratio

pg. 27

Fractals

ystems

IRREGULARITIES

In Natural Systems

Turing Patterns Redundancy

Michael Clarke

pg. 28

Brief_01: Learn

Self-Organising Systems Natural Efficiency ‘Self-organization is the process where a structure or pattern appears in a system without a central authority or external element imposing it through planning. This globally coherent pattern appears from the local interaction of the elements that make up the system, thus the organization is achieved in a way that is parallel (all the elements act at the same time) and distributed (no element is a central coordinator).’ There are countless examples in nature of systems that are self-organising. The idea has been around for centuries that given enough time, order will always appear without the need for any external organising force. It was never prescribed as a complete certainty but observed as trends. It is a central theory to the explanation of biological systems. In the 18th Century, ’naturalists’ sought out the ‘universal laws of form’. The hunt for a universal set of laws was continued in the early twentieth century. It is now considered that there are a set of laws derived from fundamental physics and chemistry that govern biological growth and form. In biological systems self-organization is a process in which pattern at the global level of a system emerges solely from numerous interactions among the lower-level components of the system. Moreover, the rules specifying interactions among the system’s components are executed using only local information, without reference to the global pattern

Dictyostelium discoideum A single-celled amoeba better known as slime mold. When they run out of food, millions coalesce into a single, slug-like creature that wanders in search of nutrients, then forms a mushroom-like stalk, scatters as spores and starts the cycle again. Research on Dictyostelium took off in the 1950s, when work by Princeton biologist John Bonner led to the discovery of a chemical used by slime mold cells to signal, triggering their group-forming behavior. At the time, scientists assumed that a few specialized cells controlled the process. But a couple decades later, inspired by famed mathematician Alan Turing’s work on how simple rules produced complex structures, researchers showed that slime complexity resulted from the linked interactions of its cells, not some centralized regulator. The image above shows the mold at its various stages searching for food.

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Physarum polycephalum Physarum polycephalum is also referred to as a slime mold although is very different to Dictyostelium discoideum. Researchers are fascinated with it’s growth properties, again in relation to searching for nutrients. The mold radiates from its centre in a network of closely linked paths exploring the territory around it. When a branch detects nutrients that branch swiftly enlarges and the branch becomes stronger. Meanwhile any branches that haven’t found anything are redundant and are killed off, fading away. This system of growing and then rationalising continues quickly forming an ef¿cient network sharing food across the network. The mold’s properties have been tested and found remarkable similarities between man made systems such as the English road network or the tokyo rail system (pictured). In these experiments, oat Àakes are placed as nodal points, such as cities or stops, and the growth of the mold is recorded. The mold’s properties are a remarkable example from nature for a self-organising system that not only creates an order from a network but is a model in ef¿ciency both structurally and at a larger scale, for ecosystems. Researchers have also found that Physarum possesses memory, and think its computational powers can be harnessed in biological computer form. The opposite page shows a natural formation of the mold outside of the laboratory. Here nutrients are available across the wood hence the less clearly de¿ned routes however there is still a clear hierarchy between the branches.

The picture to the left illustrates the maze-solving abilities of Physarum polycephalum. Due to its ability to grow ef¿cient systems when placed in a maze with multiple routes and dead ends the mold will eventually work out the fastest route killing off any detours or dead ends.

We have already looked at Frei Otto’s work on minimal path networks and minimal detour systems. The mold shows an organic instance of this phenomena in practice.

Each image is as follows: a. Structure of the organism before ¿nding the shortest path. Blue lines indicate the shortest paths between two agar blocks containing nutrients: Į1 (4151 mm); Į2 (3351 mm); ȕ1 (4451 mm); and ȕ2 (4551 mm). b. Four hours after the setting of the agar blocks (AG), the dead ends of the plasmodium shrink and the pseudopodia explore all possible connections. c. Four hours later, the shortest path has been selected. Plasmodium wet weight, 90 +/- 10 mg. Yellow, plasmodium; black, "walls" of the maze; scale bar is 1 cm. d. Path selection. Numbers indicate the frequency with which each pathway was selected. "None:" no pseudopodia (tubes) were put out. See Supplementary Information at the Nature website noted in the Bibliography for an animated versions of 2.a-c. (Nakagaki, et al., 2000.)

Michael Clarke

pg. 30

Brief_01: Learn

Cellular Formation

Molecular Crystals

Following on from self-organising systems I have looked at other biological or physical conditions that give rise to growth within a system. Obvious examples are crystal structures but I have tried to look at examples where the growth is temporary or the crystal comes together in a unique way to other elements. I have also explored brieĂ&#x20AC;y how cell like structures can be constructed from a simple change in state.

These crystals contain recognizable molecules within their structures. A molecular crystal is held together by noncovalent interactions, like van der Waals forces or hydrogen bonding. Molecular crystals tend to be soft with relatively low melting points. They are also poor conductors of electricity basically due to the lack of electrons and ions in these solids. Due to their weak physical bonds many molecular crystals can be broken down relatively easy even with small Ă&#x20AC;uctuations in temperature. Ice crystals and sugar crystals are two such examples. I like the potential for structures with limited lifetimes. Ice is already used for the construction of the ice hotel in Swedish Lapland. Every year the hotel is completely rebuilt for the winter season using the readily available resources. In Summer the whole structure simply melts away.

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Development of convection Convection cells in a gravity ¿eld The experimental set-up uses a layer of liquid, e.g. water, between two parallel planes. The height of the layer is small compared to the horizontal dimension. At ¿rst, the temperature of the bottom plane is the same as the top plane. The liquid will then tend towards an equilibrium, where its temperature is the same as its surroundings. (Once there, the liquid is perfectly uniform: to an observer it would appear the same from any position. This equilibrium is also asymptotically stable: after a local, temporary perturbation of the outside temperature, it will go back to its uniform state, in line with the second law of thermodynamics). Then, the temperature of the bottom plane is increased slightly yielding a Àow of thermal energy conducted through the liquid. The system will begin to have a structure of thermal conductivity: the temperature, and the density and pressure with it, will vary linearly between the bottom and top plane. A uniform linear gradient of temperature will be established. (This system may be modelled by statistical mechanics). Once conduction is established, the microscopic random movement spontaneously becomes ordered on a macroscopic level, forming Bénard convection cells, with a characteristic correlation length. Convection features The rotation of the cells is stable and will alternate from clockwise to counter-clockwise horizontally; this is an example of spontaneous symmetry breaking. Bénard cells are metastable. This means that a small perturbation will not be able to change the rotation of the cells, but a larger one could affect the rotation; they exhibit a form of hysteresis.

A colloidal crystal is an ordered array of colloid particles, analogous to a standard crystal whose repeating subunits are atoms or molecules. A natural example of this phenomenon can be found in the gem opal, where spheres of silica assume a close-packed locally periodic structure under moderate compression. Bulk properties of a colloidal crystal depend on composition, particle size, packing arrangement, and degree of regularity. Colloidal crystals are receiving increased attention, largely due to their mechanisms of ordering and self-assembly, cooperative motion, structures similar to those observed in condensed matter by both liquids and solids, and structural phase transitions. Polycrystalline colloidal structures have been identi¿ed as the basic elements of submicrometre colloidal materials science. Molecular self-assembly has been observed in various biological systems and underlies the formation of a wide variety of complex biological structures. This includes an emerging class of mechanically superior biomaterials based on microstructure features and designs found in nature.

(Left): A collection of small 2D colloidal crystals with grain boundaries between them. Spherical glass particles (10 ȝm diameter) in water. (Right): The connectivity of the crystals in the colloidal crystals to the left. Connections in white indicate that particle has six equally spaced neighbours and therefore forms part of a crystalline domain.

Moreover, the deterministic law at the microscopic level produces a non-deterministic arrangement of the cells: if the experiment is repeated, a particular position in the experiment will be in a clockwise cell in some cases, and a counter-clockwise cell in others. Microscopic perturbations of the initial conditions are enough to produce a (nondeterministic) macroscopic effect. This inability to predict long-range conditions and sensitivity to initial-conditions are characteristics of chaotic or complex systems (i.e., the butterÀy effect). If the temperature of the bottom plane was to be further increased, the structure would become more complex in space and time; the turbulent Àow would become chaotic. Convective Bénard cells tend to approximate regular right hexagonal prisms, particularly in the absence of turbulence, although certain experimental conditions can result in the formation of regular right square prisms or spirals. The Rayleigh–Bénard Instability Since there is a density gradient between the top and the bottom plate, gravity acts trying to pull the cooler, denser liquid from the top to the bottom. This gravitational force is opposed by the viscous damping force in the Àuid.

Michael Clarke

pg. 32

Brief_01: Learn

Self-assembly Biological systems Molecular self-assembly is crucial to the function of cells. It is exhibited in the self-assembly of lipids to form the membrane, the formation of double helical DNA through hydrogen bonding of the individual strands, and the assembly of proteins to form quaternary structures. Molecular self-assembly of incorrectly folded proteins into insoluble amyloid ¿bers is responsible for infectious prion-related neurodegenerative diseases. Nanotechnology Molecular self-assembly is an important aspect of bottom-up approaches to nanotechnology. Using molecular self-assembly the ¿nal (desired) structure is programmed in the shape and functional groups of the molecules. Self-assembly is referred to as a ‘bottom-up’ manufacturing technique in contrast to a ‘top-down’ technique such as lithography where the desired ¿nal structure is carved from a larger block of matter. In the speculative vision of molecular nanotechnology, microchips of the future might be made by molecular self-assembly. An advantage to constructing nanostructure using molecular self-assembly for biological materials is that they will degrade back into individual molecules that can be broken down by the body. DNA nanotechnology DNA nanotechnology is an area of current research that uses the bottom-up, self-assembly approach for nanotechnological goals. DNA nanotechnology uses the unique molecular recognition properties of DNA and other nucleic acids to create selfassembling branched DNA complexes with useful properties. DNA is thus used as a structural material rather than as a carrier of biological information, to make structures such as two-dimensional periodic lattices (both tile-based as well as using the “DNA origami” method) and three-dimensional structures in the shapes of polyhedra. These DNA structures have also been used to template the assembly of other molecules such as gold nanoparticles and streptavidin proteins.

The top image is a ‘glass’ like structure constructed by a marine sponge. It is built up molecule by molecule. This and other similar structures have prompted research into replicating not only biological structures but the way they are built. Within the DNA of the sponge the coding for the overall structure is kept and scientists are looking at ways of using DNA to ‘program’ self assembly. The image above shows a protein strand self-assembling into its functional state.

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The top image shows binary nanoparticle superlattices selfassembled from different combinations of semiconductor, magnetic, metallic and dielectric nanocrystals show amazing structural diversity. The insets show sketches of the superlattice unit cells.

Other forms of self-assembly are hydrogen bonds in many molecules (above) and (left) worm like micella formations. Above is a man made nano structure using Platinum. Platinum is used as a catalyst in fuel cells but is very expensive. To increase the effectiveness and therefore reduce the cost the surface area needs to be maximised. This is done at a nano level. The nano spheres are coated with an organic material called a ligand to stop them clumping. This also allows the metal to be dissolved in a solution containing long chain polymers which form a structured building block of carbon when heated. The Carbon can then be dissolved leaving the structure above. Although not an organic self assembly it highlights an approach to maximising material properties at a nano level.

The model to the left is an analogue physical representation of the self assembly found in viruses, also akin to other complex biological organisms. c. is a stage by stage photo of the model in action. The parts of the virus are constructed from a solid printer with small magnetic charges representing the forces of attraction. The â&#x20AC;&#x2DC;virusâ&#x20AC;&#x2122; then assembles itself simply by shaking the container. Other modes of self assembly include capillary forces such as the tendency of objects in water to group together. Another analogy would be cereal in milk.

Michael Clarke

pg. 34

Brief_01: Learn

Collective Behaviours - Emergence I have already looked at the principles behind self assembly and self-organisation at a micro and nano level. In each instance there is no controlling inÀuence from either a central or top down source or a knowledge of the overall system. This can be translated to larger systems and into animal behavioural patterns. I could have looked at hundreds of examples but I have chosen just a few to explain the process. Ants Ants are fascinating as a species. They have survived for millions of years with the oldest specimens of closely related species found are around 80 million years old. They possess an instinct for what needs to be done for the good of the colony and are a very social species. Every ant in a colony has a function. This is based on a number of factors all of which are aiming to ensure the long term survival of a colony. Foragers hunt for food for the colony, these tend to be the older ants as foraging is a dangerous task. They are smaller than soldiers who are in charge of defending the colony, also made up of the older ants. The younger ants will stay closer to the queen and look after the brood. Most of the ants in the colony are also female and mainly infertile. The fertile females will breed and become the queen’s of new colonies. The males contribute little to the colony until it is time to breed and they usually die shortly afterwards. Male ants come from unfertilised eggs meaning they only carry half a complement of genes all from the mother. Females will end up with half from the mother and half from the father. Given that the father only carries a half gene complement all workers will receive the same half complement meaning that they are at least 50% related to each other. It has been said that this helps the communal aspect of the species lives. This means that the majority of their make-up and their delegation skills ensure the colony continues to grow and work together to ensure survival. The other major factor behind this is communication. In this regard ants function not too unlike the slime molds I looked at earlier. They constantly leave signals for each other through chemicals secreted from the body as well as tapping and climbing over one another when passing. These signals range from alarm, sexual communication, or directly for a group effect. Much like the mold they also signal when a food source has been found. In this way an ant can follow its own route again or signal to others. These ‘branches’ of chemicals allow networks of movement to be set up to quickly harvest a food source and distribute it back in the colony. It can also signal to others to join the task. It is this collective, altruistic, nature that has ensured the successful survival of the species for so many years.

Flocking ‘From the perspective of the mathematical modeller, “Àocking” is the collective motion of a large number of self-propelled entities and is a collective animal behaviour exhibited by many living beings such as birds, ¿sh, bacteria, and insects. It is considered an emergent behaviour arising from simple rules that are followed by individuals and does not involve any central coordination.’ There have been attempts made to model ‘Àocking behaviours’ in order to better understand. It follows on from Alan Turing’s ideas about a simple set of rules generating complex systems. I will look at Turing’s work in biology later. Basic models of Àocking behavior are controlled by three simple rules: Separation - avoid crowding neighbours (short range repulsion) Alignment - steer towards average heading of neighbours Cohesion - steer towards average position of neighbours (long range attraction) With these three simple rules, the Àock moves in an extremely realistic way, creating complex motion and interaction that would be extremely hard to create otherwise. Shoals of Fish Fish exhibit much the same behaviour as birds, in particular migratory ¿sh heading for mating grounds. Shoaling is the collection of a group for social reasons and schooling is the collection for a heading or directional goal. It is a common phenomenon for dealing with predators. In much the same way as ants collective behaviour ensures the survival of the species as a whole, shoaling can limit the success of predators.

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Top left: Leaf-cutter ants working together to harvest food supplies. Above: Terns Ă&#x20AC;ock in huge numbers at certain times of year Left: Migratory birds commonly exhibit a v-shaped formation when Ă&#x20AC;ying. Right: Fish shoaling in a tornado shape.

Michael Clarke

pg. 36

Brief_01: Learn

Natural Structures - Natureâ&#x20AC;&#x2122;s Architects As Frei Otto and Buckminster Fuller did, a lot can be learnt by looking not just at behavioural patterns, but at organic structures in the world around us. I have already looked at structures that form chemically such as crystals or the soap Âżlms studied by Otto but there are also structures built from elements by animals. Termite Mounds Honeycomb Spiders Webs

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Michael Clarke

pg. 38

Brief_01: Learn

The Golden Ratio The golden ratio has inÀuenced mathematicians, artists, musicians, biologists and philosophers for centuries. It is most often studied as part of aesthetics due to it’s supposedly being the perfect composition of elements to the eye.

It is said that the ancient egyptians used the golden ratio (or phi) in the design of the pyramids and it was de¿nitely used in ancient greek architecture, most notably on the parthenon. Plato considered it the key to the physics of the cosmos and Euclid is the ¿rst known reference to splitting up a line in to the extreme and mean ratio, equivalent to what was later described as phi. It has many links to the ¿bonacci series of numbers discovered circa 1200AD. This is a series of numbers where the next number in the series is the sum of the addition of the previous two numbers. 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, etc. It also has the properties that if you divide a number by its preceding number in the series it approximates the golden ratio. The higher up the series the closer it gets. It wasn’t taken up again by any great measure until the renaissance. The renaissance brought a fascination with the rediscovery of geometries and aesthetics as well as the introduction of perspective amongst many other elements. Renaissance artists, in particular Leanardo Da Vinci used it in all their work. ‘It wasn’t until the 1900’s that American mathematician Mark Barr used the Greek letter phi to designate this proportion. By this time this ubiquitous proportion was known as the golden mean, golden section and golden ratio as well as the Divine proportion. Phi is the ¿rst letter of Phidias (1), who used the golden ratio in his sculptures, as well as the Greek equivalent to the letter “F,” the ¿rst letter of Fibonacci. Phi is also the 21st letter of the Greek alphabet, and 21 is one of numbers in the Fibonacci series.’ In 1970 Roger Penrose discovered how surfaces could be tiled in ¿ve-fold symmetry called ‘penrose tiling’ using shapes found in a pentagon and pentagram with the ratios of phi, 1 and 1/phi. Discoveries are still being made today that have a basis on the golden mean, section or ratio. Daniel Shechtman has just been awarded the Nobel Prize for chemistry this year for his discovery of quasicrystals that he originally found in the 1980s but is only just been recognised today.

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Examples found in nature and phyllotaxis There are countless examples of the golden ratio in nature. The spiral that can be drawn through a series of golden rectangles, also the ¿bonacci series is a logarithmic spiral and can be found in plant leaf formation such as the one above and perhaps best known in nautilus shells as the photo on the left demonstrates. The series can also be found in tree branching and many ratios of the human body such as the bones in the ¿nger. There are really interesting examples from phyllotaxis. ‘In botany, phyllotaxis or phyllotaxy is the arrangement of leaves on a plant stem (from Ancient Greek phýllon “leaf” and táxis “arrangement”)’ This can be in several forms but a spiralling effect is one common form found in nature exhibiting similar ratios of curve to the golden section. Particularly stunning examples come from alternate spirals such as the seeds on a sunÀower head.

Images clockwise from bottom left: Bottom left: The Mona Lisa by Leanardo da Vinci is said to be based on ‘De Divina Proportione’ or the divine proportions Top left: Central seed pods in many Àowers exhibit spirals in the golden ratio. Top: The Vitruvian Man by Leanardo da Vinci. Also based on divine proportions setting out ratios in the body. Top right: The Parthenon in Athens is set out according to the laws of aesthetics. This includes the golden ratio but also ellipsis, where columns at the edges lean slightly more than at the centre and the steps are curved in order to appear straight to the human eye Bottom right: the great Pyramids in Egypt. These are set out to align with the stars but are also said to be constructed using phi and pi.

Michael Clarke

pg. 40

Brief_01: Learn

Irregularities and Chaos in Nature Many of the examples over the next few pages deal with irregularities in nature and randomness or redundancy in natural systems or phenomena. This does not mean, however, that these examples cannot be described mathematically or predicted partially. In many cases such as fractal geometries and Brownian motion there are accurate mathematical models to predict the sequence of events or the trend despite the chaotic nature of both. It is an exploration of this chaotic nature that I am looking at over the next few pages. Although when transferring examples from nature to built structure we often look for the most ef¿cient system, to minimise material use and impact I believe there are examples of chaos in nature that we can learn from. No engineering solution proposes a structure constituting of the bare minimum. There have to be fail-safes or redundancies built in.

Simple Rules For Complex Systems Alan Turing was a mathematician who developed a method of calculation based on very simple rules. He is largely known for his work in computing and is the father of the ¿rst computing machine, the Turing machine. However he applied his ideas into biology also. Again using a simple set of rules he believed complex forms could be simulated. He de¿ned a set of rules to create patterns using a ‘reaction-diffusion system’. The system consists of an “activator,” a chemical that can make more of itself; an “inhibitor,” that slows production of the activator; and a mechanism for diffusing the chemicals.

A Photo of Alan Turing alongside some examples of Turing Patterns created by mathematical models. They work based on the reaction-diffusion system that Turing devised. Many graphical manipulation softwares have functions built in to sharpen and blur an image. These are based on similar mathematical models of approximation. To the left is an image of a nautilus shell. Below is the same image that I have just applied a sharpen ¿lter followed by a blur ¿lter over and over again.

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Turing Patterns found in nature alongside mathematical models using the basic principles. The patterns found are remarkably similar.

Turing Patterns in 3D Researchers have tried to prove whether Turing patterns can be found in the origins of complex structures such as lungs or limbs. One way is to set off chemical reactions that cause Turing patterns in Ă&#x20AC;asks in the laboratory. The above images are from a group of researchers led by Brandeis University chemist Irving Epstein. They are created using tomography, a form of imaging used to reconstruct three-dimensional images from thousands of two-dimensional snapshots, to picture them.

Michael Clarke

pg. 42

Brief_01: Learn

Fractal Patterns Fractal patterns can be found everywhere in nature. Many things that appear to have some kind of repetitive or iterative nature yet look completely random can be described using a set of rules called fractals. The mathematics behind fractal geometries is relatively simple as with the rules in the Turing patterns but can lead to beautiful individual forms. Fractal patterns are the result of recursive functions and can be said to continue indeÂżnitely. There are countless examples found in nature that often result in beautiful organisms or phenomena. There is also a large area of mathematical study into fractal geometry. One pattern that is often drawn is the mandelbrot set. This is a collection of numbers that exhibit the same property, they do not grow exponentially when given an input number of any value within the complex plane for the iterative function f(x) = xÂ˛ + c. Although this is a very simple function the mandelbrot set of numbers is inÂżnite and produces a spiralling pattern.

Fractals in living biological systems Pictured are just two examples of fractals found in living organisms. Above is an image of romanesque broccoli. This grows in spiral patterns also linked to the golden ratio however each spiral is a collection of smaller spirals repeating in a nature very similar to other fractal patterns. Many plants grow in what appears to be simple recursive functions including leaf venation and branching.

pg. 43

Fractals in the weather

Fractals in the Earth

Lightning is just one example of fractals found in weather patterns. Lightning strikes are not predetermined but work out a path of least resistance to the ground changing direction step by step.

The above image is of a salt Àat. The ridges across the top show a consistent yet random pattern. It is characteristic of fractal patterns.

Cloud vortex’s like the one to the left also exhibit recursive patterns. They have similarities to many mathematical models for attractors and some links to chaos theory which can be seen on the next page.

Other patterns occur at a much grander scale such as mountain ridges pushed up by the earth and weathered leaving fractal patterns. Similar patterns can be seen in river valleys or gorges where water has carved out routes through the earth.

SnowÀakes are a beautiful example of naturally occurring fractals. The koch snowÀake was the ¿rst identi¿ed fractal curve. SnowÀakes also exhibit a crossover with self-organising systems being a molecular crystal as I looked at before.

Michael Clarke

pg. 44

Brief_01: Learn

Randomness and Redundancy Chaos Theory I mentioned how we can begin to predict seemingly random patterns mathematically but that these patterns are still important. Although seemingly chaotic it can often be beautiful and add visual interest. ‘Chaos theory is a ¿eld of study in mathematics, with applications in several disciplines including physics, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the butterÀy effect. Small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes for chaotic systems, rendering long-term prediction impossible in general. This happens even though these systems are deterministic, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved. In other words, the deterministic nature of these systems does not make them predictable. This behavior is known as deterministic chaos, or simply chaos. Chaotic behavior can be observed in many natural systems, such as the weather. Explanation of such behavior may be sought through analysis of a chaotic mathematical model’ ‘Chaotic dynamics In common usage, “chaos” means “a state of disorder”. However, in chaos theory, the term is de¿ned more precisely. Although there is no universally accepted mathematical de¿nition of chaos, a commonly used de¿nition says that, for a dynamical system to be classi¿ed as chaotic, it must have the following properties: it must be sensitive to initial conditions; it must be topologically mixing; and its periodic orbits must be dense. The requirement for sensitive dependence on initial conditions implies that there is a set of initial conditions of positive measure which do not converge to a cycle of any length.’

Brownian Motion ‘Brownian motion (named after the botanist Robert Brown) or pedesis (from Greek: ʌȒįȘıȚȢ “leaping”) is the presumably random drifting of particles suspended in a Àuid (a liquid or a gas) or the mathematical model used to describe such random movements, which is often called a particle theory.’ Brown was studying pollen grains of the plant Clarkia pulchella suspended in water under a microscope when he observed minute particles, ejected by the pollen grains, executing a jittery motion. By repeating the experiment with particles of inorganic matter he was able to rule out that the motion was life-related, although its origin was yet to be explained. Einstein was the ¿rst to look at Brownian motion and used it as proof in his kinetic theories to con¿rm the existence of atoms and molecules. Ink in water

pg. 45

Cellular Automata - Conway’s Game of Life ‘Rules of the Game of Life Life is played on a grid of square cells--like a chess board but extending in¿nitely in every direction. A cell can be live or dead. A live cell is shown by putting a marker on its square. A dead cell is shown by leaving the square empty. Each cell in the grid has a neighborhood consisting of the eight cells in every direction including diagonals. To apply one step of the rules, we count the number of live neighbors for each cell. What happens next depends on this number. A dead cell with exactly three live neighbors becomes a live cell (birth): An image from Conway’s Game of Life - Many people search for patterns to try and apply to other problems. The above pattern oscillates between three patterns no matter how many iterations. A live cell with two or three live neighbors stays alive (survival):

In all other cases, a cell dies or remains dead (overcrowding or loneliness):

An image of a cellular automata pattern called the Sierpinski Triangle. Inside each white triangle are three further triangles. Like fractals this pattern is in¿nite.

Attractors

Note: The number of live neighbors is always based on the cells before the rule was applied. In other words, we must ¿rst ¿nd all of the cells that change before changing any of them. Sounds like a job for a computer! Life is one of the simplest examples of what is sometimes called “emergent complexity” or “self-organizing systems.” This subject area has captured the attention of scientists and mathematicians in diverse ¿elds. It is the study of how elaborate patterns and behaviors can emerge from very simple rules. It helps us understand, for example, how the petals on a rose or the stripes on a zebra can arise from a tissue of living cells growing together. It can even help us understand the diversity of life that has evolved on earth.

If you start with a point in space and plot the orbits of attractors it is relatively easy to build up a picture of what the end system will look like. ‘The Lorenz attractor (pictured) is perhaps one of the bestknown chaotic system diagrams, probably because it was not only one of the ¿rst, but it is also one of the most complex and as such gives rise to a very interesting pattern which looks like the wings of a butterÀy.’

In Life, as in nature, we observe many fascinating phenomena. Nature, however, is complicated and we aren’t sure of all the rules. The game of Life lets us observe a system where we know all the rules. Just like we can study simple animals (like worms) to discover things about more complex animals (like humans), people can study the game of Life to learn about patterns and behaviors in more complex systems. An image from an interesting script I found online that translates time in Conway’s game of life 3 dimensiponally in the z-axis. This builds up a city representation of the patterns. The large diagonals are from gliding pattenrs that keep moving away from their start.

The rules described above are all that’s needed to discover anything there is to know about Life, and we’ll see that this includes a great deal. Unlike most computer games, the rules themselves create the patterns, rather than programmers creating a complex set of game situations.’

Michael Clarke

pg. 46

Brief_01: Learn

pg. 47

Experimentation Looking into Frei Ottoâ&#x20AC;&#x2122;s ideas about minimal path systems and exploring these through my own analogue and digital experimental models. Learning grasshopper as a parametric tool for form Âżnding exploration.

Michael Clarke

pg. 48

Brief_01: Learn

Digital Experimentation I started to explore branched structures in grasshopper. Although grasshopper doesn’t deal with recursive functions I have simply replicated commands using copy and paste to create further branches. The model documented on this page allows full control over the branch positions, length and thicknesses. It also allows the end to be changed and individual control across each branch however it loses a degree of quick change by making each component individual. It would be good to look at a plug in to deal with looping functions and start to look at scripts that allow a more organic growth and mutation into the growth. My next experiments will look at trying to replicate Fuller’s minimal path branches by modelling separate threads and looking at attraction forces with kangaroo. The model Although the image to the right shows a huge branching set of de¿nitions. The ¿rst grouped column de¿nes the trunk of the ‘tree’ structure. A simple line with thickness and direction and a de¿ned control point along the curve, currently placed at the end.

The second group of commands is the ¿rst set of 4 branches. A vector controls the direction of each branch and then each branch is de¿ned by the original command for the trunk copied over. The third column is the second column replicated a further four times. A looping function would remove the need for this column entirely.

pg. 49

Changing the height of each branch is simply controlled by a slider attached to the construction line surface befpore each line is given a thickness.

Changing the radius of the branch cylinders or thickness of each branch. The top slider controls the radius of the cylinder around the construction line and the bottom cylinder controls the capping. The end capping to each branch can also be switched between rounded, capped or open.

Changing the angles with a vector based control. I have not worked out a way of allowing an angle to be de多ned but this is a simple method of de多ning a direction using x, y and z values. By introducing a slider to the z direction the vertical angle can be altered. The image shows the same tree from the model with every variable altered at some point that can be.

Michael Clarke

pg. 50

Brief_01: Learn

Analogue Experimentation Self-Organising_01 I wanted to test Frei Otto’s minimal path experiments myself as a basis for my research. I started by initially looking at minimal paths as a branch structure. The aim was to replicate Frei Otto’s experiment and those of his students at the Institute of Lightweight structures and then expand on them to see what other inÀuences and factors could be calculated through similar experiments. This page documents my ¿rst attempt to replicate Otto’s experiment. I constructed a frame that could allow a number of iterations of comparable circumstances. Threaded rods were used to separate two sheets of acrylic acting as a base approximately 230mm apart. In both sheets of acrylic are 16 metal ¿xings removed from electrical connectors laid out in a regular grid, 4 ¿xings by 4. These ¿xings have two screws, one to attach the ¿xing to the acrylic, one to clamp the wool threads in place. In the initial model, threads were ¿xed in place from one ¿xing on the top sheet of acrylic to the corresponding ¿xing on the acrylic base with the minimal length of thread between the two creating 16 vertical, taught threads. The threads were then lengthened by 10% and then 20% before being dipped in water. I encountered a number of problems with this method which have been documented on this sheet. The major problem with my setup was the attraction between the threads. After dipping the model in water with a 10% extra length I was not getting any branching. I tried 20% extra length with limited success before realising that after pulling the thread from the water, the weight of the wet wool meant the extra length was weaving around the base before ¿nding the shortest route to the top, largely straight lines all separate from one another. I knew that a minimal path system would converge to a single ‘trunk’ before beginning to branch out so in order to carry out an experiment into these branches I ¿xed all the threads into a single point just off the base using a ring of copper wire before dunking the model again in water. I then tried dunking the model in the water the other way up with the ¿xed point at the top of the model. This produced a result with clearly de¿ned branches. The model is also affected by gravity after organising. The weight of the threads when wet produces sagging and begins to separate when the ¿xed point is at the base of the model.

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01. The initial frame model with minimal length connections 02. Detail of the 多xings 03. Dipping the model into water 04. 10% additional length between points. A lot of the threads have stuck 多rst to the acrylic before rising and have not grouped at all. 05. 20% additional length between points. Again, most of the additional length that is supposed to allow the minimum paths to form has been lost to gravity on the base plate however there is some form of branching beginning to appear. 06. The threads have been 多xed to a single point at one end, suspended from that point at the top of the model. The resulting structure is a lot more clearly de多ned into a single branching network. the furthest distance threads have lost the additional length however and are simply straight. 07. When turned up the right way many of the threads have separated and sagged under gravity

Michael Clarke

pg. 52

Brief_01: Learn

Analogue Experimentation Self Organising_02 The next aim is to try and harden the resulting structures from my previous experiment. I can then remove them from the frame and try another method or altering some of the initial settings. I would like to try the experiment with a lot more threads in closer proximity to one another to try and observe branching without ¿xing a point. Due to the threads natural attraction to the acrylic it may still be necessary to ¿x points. It may also be interesting to look at different lengths or additional threads attached to the existing threads to provide separate branches as in leaf veins. In this experiment I have used an expoxy glosscoat. This is a clear resin that can be painted on and can dry at really thin amounts of resin suitable for my branches. I had dif¿culty painting it on all areas of the resultant structures. Particularly due to the threads being wet and the dif¿culty in getting a slow-drying resin to cover all areas without running down the length of the models. In the end I managed to get it to work but had to chop a lot of the connectors free and use new ones for the additional models. The ¿nal results are strong enough to stand alone. In this way I could produce a whole series of ‘optimised’ networks, each one unique.

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01. Painting the models with resin as soon as they came out of the water - dif¿culties arose from trying to capture the optimised networks before they sagged. 02. A close up of the resin setting into the joints of the model. 03. The ‘sagged’ result from the ¿rst experiment standing alone 04. Even after setting the resin was not completely rigid and sagged slightly when turned the other way up. 05. The result from the ¿rst experiment that was suspended from the top producing a much clearer branching structure. However, it is evident where the threads have been tied together has not left enough slack for the threads at the edges to group. Starting from a single point initially may ¿x this.

Michael Clarke

pg. 54

Brief_01: Learn

Analogue Experimentation Self-Organising_03 I have followed up my smaller thread models with a 1:1 scale model. I wanted to se if similar principles of self-organisation could be explored at a much larger scale and in dry conditions. Essentially, it is not possible to ‘dip’ an entire room in water to allow the threads to bunch into minimal paths. I started by creating a basic model that I could then use as a tool for various methods of organisation. The model has a grid like set of threads across a small area of the studio space above head height. This was intended to provide some kind of logic to the placement of the vertical threads rather than hanging randomly however I didn’t want to build a large supporting framework. Therefore the threads are ¿xed by tying at 4 points to any available ceiling ¿xture or simply taped to the wall where no obvious connection was available. This makes the initial grid’s rigidity dependent upon the tension achieved across the grid between the ¿xing points. As the hanging threads can build up a large amount of weight and the ¿xings of the grid (where taped) are relatively unstable the grid sagged into a shell like support. I do not think that this will seriously affect my explorations of the model. My initial experiment was a controlled bunching of the threads by myself and therefore not self organising. This was informed by my earlier analogue models and I simply grabbed the threads in certain places to achieve a branched structure. Although not self-organising it was an early test of what I hoped to achieve later. I believe that the bunching achieved is a result of the friction between the ¿bres of the threads and not of any natural attraction forces occurring. I would like to use the rest of the grid to try two further methods of self organisation, the ¿rst using electrostatic properties and the second using electromagnetic properties. For the ¿rst example I will need thread with less wool content, maybe nylon and additional items to help charge such as polythene rods or balloons. For the second I will need ¿lament wire and a power supply capable of producing suf¿cient current.

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01. The initial grid for hanging the threads, already sagging from the weight of a few threads. 02. The model in it’s starting state in the corner of the room. Threads are hung at regular intervals from the grid above. 03. The ¿rst set of bunching from the top down, I grouped the threads into small groups about a third of the way down. 04. The second set of bunching taking several groups from the ¿rst bunch and combining two thirds of the way down the length of the threads. 05. The ¿nal set of bunching combined all of the ‘branches’ into one base point or ‘trunk’. 06. Another view of the resulting network or structure.

Michael Clarke

pg. 56

Brief_01: Learn

Analogue Experimentation Self-Organising_04 After the large scale model I returned to the smaller models to explore further hoping to improve upon my earlier attempts by using a higher wool content thread much more closely packed. I thought the wool might trap more air however it absorbed just as much water and was quickly to heavy to bunch properly without being affected by gravity and again, sticking to the acrylic base. However I used this model to experiment with different ways of doing it. The ¿rst replicates my analogue experiment 01 simply with 36 threads instead of 16. I then turned the top sheet of acrylic 90° to try and get more of a crossover between the threads but again a similar result was achieved. The ¿nal images show a piece of wire tying the threads into a node as in experiment 01 however this time in the middle of the model. It demonstrates clearly the effect of gravity on the experiment. Theoretically, an optimised system, although not exactly the same should have a similar result both above the node and below, simply mirrored. However, in this model, above the node has sagged and below has bunched but also across the base plate. The ¿nal image is the same model simply turned on it’s side. Again the weight of the threads is evident from the arches appearing.

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01. The initial grid for hanging the threads, with extra length to allow for bunching. 02. The ¿rst attempt at dipping it in the water, shows similar problems to the ¿rst experiment with less threads. 03. Second attempt at dipping it in the water 04. The model after being dipped in water with an arti¿cial node placed in the centre. Notice the clumping below the node and the sagging above. 05. The ¿nal model turned on it’s side.

Michael Clarke

pg. 58

Brief_01: Learn

Analogue Experimentation Self-Organising_05 Learning from the earlier experiments I made another quick model using only a single base point connected to all the points above. The results are much clearer and show a coherent minimal path system. I have then adapted the model by adding smaller threads to each original thread before dipping it in water again. I wanted to test whether or not they would join to form a secondary path system on top and if they interconnected or simply stuck to the existing paths. This was not so successful and needs further testing. I would like to use a 多ner thread for the secondary network and create slightly longer threads with more of them.

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01. The initial set up with all the threads pulled taught. 02. The model with additional length to each thread to allow for bunching. 03. Front view after dipping the model in water. 04. Side view after dipping the model in water. 05. The dry set up with additional threads tied. 06. A close up of the â&#x20AC;&#x2DC;secondary threadsâ&#x20AC;&#x2122; after being dipped in water.

Michael Clarke

pg. 60

Brief_01: Learn

Attraction:

Digital Experimentation Self-Organising_01

The three diagrams here show an attraction force applied to two parallel lines. 01. shows two equal length lines with a uniform force acting between the points. This produces a symmetrical deÀection between the points.

Using a combination of Kangaroo and Grasshopper for Rhino I can begin to construct a simple self organising computer model based on my thread experiments. Although not quite dealing with the same forces I have started by looking at bunching models replicating my threads but instead subdividing them into lengths of connected springs.

02. The ¿rst line is half the length of the second and offset so that the start point of each line are aligned. The result is an asymmetric bunching at neither midpoint.

To explore the fundamentals I have started with two simple parallel lines. Each line is subdivided into points with a spring between them. A force is applied using Kangaroo interacting between all of the points in the system. The strength of the force can be altered to be positive (repulsion) or negative (attraction). A cutoff value can also be de¿ned to limit the distances that the force acts between. In each experiment the end points are ¿xed in order to limit the system to stop it collapsing to a point under an attraction force or expanding out continuously under repulsion.

03. The same lengths of lines as 02. with the mid points aligned. This produces a bunching about the middle with the point of connection as a peak in two parabolic curves.

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pg. 61

03.

Repulsion:

Basic bunching across a 2x2 grid

These three diagrams are replicating the initial conditions of the ¿rst three with a repulsion force instead of an attraction force. Again the endpoints are ¿xed to control the system.

In this system instead of 2 parallel lines I’ve added an additional 2 parallel lines above to form a uniform 2x2 grid. The images show the force acting on the curves from the initial starting condition to the ¿nished bunching. Here the bunching converges along a line central to the initial grid, equidistant from each of the imaginary boundary faces.

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Michael Clarke

pg. 62

Brief_01: Learn

Digital Experimentation Self-Organising_02 These experiments follow on from the 多rst set using the same initial set ups. In each of the series the cut off for the attraction forces applied is set to just over the length between two lines. In each case the set up is using lines of the same length.

pg. 63

Changing the cutoff values The examples below use the same set ups as the sequences to their left. In each case the cut off has been doubled to be just over double the length between two strings. With this number of initial threads it has the impact of combining trees to a single branch as opposed to 2 or four separate branches collectively. It would be interesting to try more than one attraction force or to vary the initial lengths. At the edges we are beginning to see separate groups before we see the overall branching. If I increase the starting length greatly it could begin to organise itself into a hierarchy of set ups.

Michael Clarke

pg. 64

Brief_01: Learn

Digital Experimentation Self-Organising_02 Grasshopper Definition

This set defines the threads used in the model as their starting position. In this case a set of points (any points can be defined) each have a line of length L (determined by the number on the slider) in the Z direction (vertically up).

This page explains the script for the previous experiment. However, the input here is for one set of threads. The forces applied and the overall de¿nition is the same as here for every output in both experiments 01 and 02 it is only the initial points and lines that are changed.

The threads are divided into a number of separate lengths (defined by the input N). The ‘Div’ command defines the domain of each subdivde. The ‘SubCrv’ defines the series of smaller lines that now make up the threads.

The threads are also divided into a series of points, also defined by n. This basically puts a point at each end of the thread and at each end of the new smaller lengths making up the threads.

The points are all connected to each other using the interconnect points command.

pg. 65

This model uses the in-built physics engine in the Kangaroo plug in for grasshopper. Kangaroo allows the input of multiple forces acting on a model and simulates the effect of those forces over time. The resulting movement of the model can be seen on the screen which is how I have generated the step by step images in the last two experiments. The threads are controlled using anchor points - fixed points that will not move whichever forces are acting on the model. In this case, these are defined as the start and end points of the full length threads. The first input force is one called springs. This defines each smaller length within the threads that we have generated as a separate spring. This gives an inherent tension to each thread. The second input force is one called PLaw. This takes all the lines connecting every point to every other point and uses them as a connection for an attraction or repulsion force to act upon. In this model the strength is set to a negative value meaning the force works as an attraction. The last input needed is the geometry to be transformed. This is a line which is made up of all the smaller lengths that we have also defined as the springs.

This toggle starts the animation when sets to false and resets it when set to true.

The final commands are purely for visual means. They take the output geometry and define a cylindrical shape following the curves generated. The cylinderâ&#x20AC;&#x2122;s radius is controlled by the slider.

Michael Clarke

pg. 66

Brief_01: Learn

Digital Experimentation Self-Organising_04 This experiment took a different approach to creating the bundling threads although with similar principles. However, instead of a series of springs the model here takes a 2D script for wool threads created by Dave Reeves. I have adjusted the 2D de¿nition to de¿ne a series of points in 3 dimensions. The script uses de¿nitions for tension, cohesion and separation in the threads that act over a period of time. Although a similar result could be achieved to my original digital experiments I have looked at making this more organic. The points at the top and bottom are randomised and the connections between the points are not necessarily the nearest connections to allow suf¿cient overlap for the threads to ‘stick’. The resulting sequence is documented numbers 01 to 05. Further images can be seen around.

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Internal perspective

pg. 67

Aerial perspective

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Front elevation

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Michael Clarke

pg. 68

Brief_01: Learn

Digital Experimentation Self-Organising_04 Grasshopper Definition This page documents the script that produced the model for the digital experiment_04. Each step is highlighted and annotated to describe the inputs, the controls and the process of organisation that the model runs through.

This slider controls the number of values taken to de多ne the starting points. It feeds into four random number generators.

These are 4 random number generators. Each one is set to a different random seed generation ensuring different values. They feed in pairs to produce the top points and the base points of the model. Each pair de多nes a points co-ordinate by x and y values.

These two sliders de多ne the domain for the random number generators. This means that all values generated by the random generators are constrained to a number between the value of these two sliders

pg. 69

This set of functions is the script made by Dave Reeves controlling the thread movement. The controls are described as follows: separative forces - operate between nodes of a single thread.

decay - controls the amount of velocity lost from one iteration to the next.

cohesive forces - operate between nodes of different threads.

0 = total velocity loss 1 = no velocity loss

tensile forces - operates between nodes of a single thread.

This box draws a line between the set of points at the base and the set at the top. Each point is connected to one corresponding point by a single line. The rotating arrow next to B is to reverse the values in the list to ensure that the lines cross.

general use seek - control active range of cohesive and separative forces. power - controls magnitude of each force

to start: disable timer, set “reset” to false, then enable timer. to reset: disable timer, set “reset” to true, set “reset” to false, then enable timer

timestep - controls rate of simulation. beware of instability with higher values. This function places a circle with it’s centre at each of the base and top points of the model as can be seen from the links between them. The radius of each circle is the active range of the separation forces. The three previews are easy toggles for viewing different outputs of the ¿nal model. The ¿rst previews the circles with a dark grey colour swatch. The second is a preview of all the points in the model including the base and top points and the divide points along each ‘thread’. The third previews the threads themselves. In this case the plug in is a ‘pipe’ surface which is basically a cylinder around the threads.

This set of functions simply measure the length of the lines produced and then divide that length by the value of the slider. This gives the number of points to place at equal intervals along each line which is the function of the ‘divide’ box. These two point controls de¿ne the points at the top and bottom of the model. The additional number slider for the bottom set of points control the overall height of the model currently set to 20.

The ‘crv’ tool stands for curve. This is redrawing the threads or lines we had before once the forces from the ‘wooly paths’ script have been applied. The pipe command following it, creates a 3D model using cylinders that follow the curves. This is what can be seen in the images on these pages.

The ¿nal set of commands are used to calculate the shadow cast by the model. The mesh command converts the pipe surface to a mesh. MShadow stands for a mesh shadow which calculates the shadow of the mesh using a light angle de¿ned by a curve (Crv). This curve is drawn in Rhino and can be rotated or moved freely depending on what light direction is desired. The Planar command simply takes the shadow output and puts a surface of the same shape in it’s place which can be rendered Michael Clarke

pg. 70

Brief_01: Learn

Digital Experimentation Self-Organising_05 This experiment builds on the last digital experiment (04) and changes the starting conditions. In this case the points are deÂżned randomly within a circular boundary at the base and the top as opposed to within a square grid. This removes points at the edges that result in one or two threads that donâ&#x20AC;&#x2122;t interact with the rest of the model. Instead of reversing the input at the top to create a model with lots of crossed threads the deÂżnition here simply rotates the points at the top creating a starting model similar to a hyperboloid revolution. This rotation can be controlled via an input command varying from 0rad to (pi)rad. The code is explained below.

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Michael Clarke

pg. 72

Brief_01: Learn

Digital Experimentation Self-Organising_06 This experiment builds on digital experiment 04. It makes another change to the starting conditions and then adds a secondary set of threads between the primary ones, similar to leaf venation although on a very simple and abstracted way. In this case, the initial points to de¿ne the primary thread network are the same as in 04 but for one small difference. Instead of reversing one set so that the threads cross, each point here links to it’s corresponding point above creating a set of vertical lines. A secondary set of threads is then added using points on the primary threads as it’s de¿nition. This builds up a lattice and a hierarchy of networks. To accentuate this, the secondary threads have been shaded blue and given a thinner radius.

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This part of the grasshopper de¿nition is the end of the same script from a previous experiment (04). The only difference is there is no crossing of threads initially to provide large gaps at the centre of the model. (see ¿g. 01.)

pg. 73

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These three sets are identical. Each one picks a curve from the initial threads and de¿nes a point a set distance along (the top slider). The bottom slider de¿nes a point a certain distance along on every thread. The Ln command draws a line from the point de¿ned by the ¿rst slider to all the points de¿ned by the second.

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This set is the same bit of script from the digital experiment 04 but this time applied to the secondary threads just created. It is played only after the result of the primary threads has been achieved.

These 多nal three commands simply visualise the resulting model and place a 3d cylindrical brach over the threads as before.

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Michael Clarke

pg. 74

Brief_01: Learn

Digital Experimentation Self-Organising_07 This experiment is simply combining the previous two experiments. It takes the circular thread network and begins to add a secondary network of threads inside.

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Michael Clarke

pg. 76

Brief_01: Learn

Digital Experimentation Self-Organising_08 This experiment takes the principles of multiple layers of threads or routes to bunch back to it’s simplest version. It is all 2D and starts by copying Frei Otto’s experiment for energy optimisation by limited detours by simply connecting points around a circle to their opposites across the diameter. I have used the same ‘wooly_paths’ script as in the previous examples to apply the bunching. Once this has ¿nished I added a series of secondary threads one at a time. In each instance a single point in the model on one thread connects to chosen point on every other thread in the model. The same ‘wooly_paths’ script is then applied to the secondary thread netwrok.

01.

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06.

Image key: All the images read as sets of three from top to bottom representing keyframes within a timescale. 01-03. The initial set of threads or primary threads. Each image is part of a sequence with 03 being the resulting model. 04-06. A single point of connections is added as the 多rst set of secondary threads. 07-09. A second set of secondary threads is added to the model. This time the two sets of secondary threads start to bunch together, each affecting the other. 10-12. A third set of secondary threads are added. 13-15. A fourth set of secondary threads are added.

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Michael Clarke

pg. 78

Brief_01: Learn

Digital Experimentation Leaf Venation_01 I came across a series of mathematical models in my research for approximating leaf venation. It would be really interesting to alter my thread experiments with objects or spaces that repulse the threads. It would be a very interesting way of doing it if these objects or spaces could come from the threads themselves almost growing out of the primary structure. I have therefore started to experiment with how leaf venation may be achieved in grasshopper. I have seen these lamp designs (below) by Nervous System before and found out that they are based on an algorithm for leaf venation. I found the set of rules that the ‘growth’ follows in a research paper by Adam Runions although no scripts for the model. I have therefore tried to replicate the algorithm using only grasshopper and it’s plugins, without writing any script myself. It is a work in progress that I hope to ¿nish once I understand the software better but here is my progress so far.

We begin following it at the stage when the vein system consists of three nodes (black disks with white centers) and there are four auxin sources (red disks) (a).

First, each source is associated with the vein node that is closest to it (b, red lines);

This establishes the set of sources that influences each node. The normalized vectors from each vein node to each source that influences it are then found (c, black arrows).

These vectors are added and their sum normalized again (d, violet arrows) Providing the basis for locating new vein nodes (d, violet circles).

The new nodes are incorporated into the venation, in this case extending the midvein and initiating a lateral secondary vein (e).

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De¿ne sources for growth towards

De¿ne root[s] on edge (blue circle) - ¿rst vein node

Link sources to closest node point (currently one)

Take the average vector for each node of all sources affecting it.

New vein node de¿ned set distance along vector.

Re-evaluate sources to their closest node point (now two nodes)

Again average vectors for each node by sources affecting it. (¿rst node now redundant - second is closest for all sources)

Re-evaluate sources to closest nodes. Two of the sources now affecting the second node, all others the third node.

Two new nodes de¿ned, a new vein branch beginning to form to the bottom of te primary vein. Michael Clarke

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