Contents
Data Trawl
Simulate
Hack / Hybridise
Data Trawl Diagrammatic Response to Summarise ‘The New Mathematics Of Architecture’ By Jane & Mark Burry
This book embraces and explains developments within architecture and design over the last 40 years. It explores the concept of ‘New Mathematics’ which fundamentally is a collection of post-17th century mathematics combined with concepts such as; imersion, developable surfaces, minimal surfaces, chaos theory, and non-euclidean geometry.
Weapons of the Gods
We no longer speak the language of the Architects of the past.
We have evolved into Architects of the future, where pencil leads becomes line weights.
Mathematics and Design
Geometry came from the Greek ‘ Land Measurement / Earth Measurement’ -subdivision / space organization - Herodotus divided Pharaohs land into equal spaces to calculate revenue received for each area.
Arithmetic - numbers
‘When Code Matters’ by Ingeborg M. Rocker ‘....everything turns into algorithms....’
Did architecture get pushed too far to the practical side and become more engineering than design? Function following Form....
Computation has unlocked a future where design can return to dominating the process while still considering all the surrounding factors . We can now create forms and use programs designed specifically to determine virtually anything from stresses and loads to environment factors .
Can everything in life be determined by a computer program??
Mathematical Surfaces and Seriality
Surface - A barrier between forms of matter and/or non-matter.
Thinness - 2D threshold between one space and another without substance or weight. ie. Graphene
Plane - Piece of a constructed Cartesian idea space (space that can only be used once created)
Single-Curvature - A developable surface that creeps up on you - not seeing everything that is there.
Self-Intersection - Klein Bottle - inside and outside cannot be distinguished between.
Curvature - A straight line has zero curvature, where as a circle has constant curvature equal to the inverse of its radius ( as radius of curve inc. curvature decreases).
Non- Euclidean - For any given infinite line a point off that line there is only one parallel like through it. However using hyperbolic geometry there are many - Eshers work.
Series - Sum of sequence of terms - order and values important.
What does this all mean in terms of architecture?? A series of algorithms program a function. These functions act as the laws upon which the programs we use to design are based upon giving a mathematical foundation to our desired creations. One algorithm could program a curves curvature in relation to its radius where as another could be used to create a surface allowing a thinness to be programmed to appear between two surfaces to allow them to join and thus begin the construction of a form
Chaos, Complexity and Emergence
- A system gives back new information from simple inputs.
Aesthetics - Pattern is our currency in understanding and interpretation of the world.
- Architects look to living organisms that acquire their complex forms and behaviour patterns through interactions with their surroundings. - Form, Shape, Growth and Scale.
Michael Batty - Thinking of cities in terms of individuals. Disaggregation - divide into parts Heterogeneity - quality of being diverse and not comparable in-kind
Materiality - Efficiency and economy of material production from natural systems. Sinosteel International Plaza in Tianjin, China, by MAD architects. The external honeycomb structure removes the need for an internal structure.
Responsiveness - A systems that truly represents the systems of environmental performance. Nano-composite Steel - structure more like plywood to reduce the brittle effect steel can have under stress - ductile strength doubled.
Chaos Theory - A system dependent upon set initial conditions and if any of the initial conditions change the outcome will be different. (Butterfly Effect)
Recursion - Process of repeating items - parallel mirror theory - Fibonacci sequence
Fractal - Self-similar pattern where it is the same from near as it is from afar.
Emergence - The way complex systems and Patterns arise out of a multiplicity of relatively simple iterations.
Genetic engineering - Shapes the process rather than directly determining the outcome. - John Johansen nano-architecture.
Packing and Tiling
Space filling - Subdividing space in ways that leaves as little as possible/ nothing at all, unaccounted. - purpose for all space.
Symmetry - same/opposite parts repeat regardless of scale.
Pattern - repeat of a particular manner. Ways of subdividing space creates patterns. - Architects must find ways to subdivide space that creates an area where nothing within the boundaries is unused.
Voroni Pattern - Veroni Cells - ways of dividing space into a number of regions. A set of points is specified before hand and regions are created responding to rules placed upon the points. (back to the idea of programming functions) - If the points were programmed to be equidistant and that the regions created would all be equal it would result in a scenario like wall tiling.
Architecture has a close interest in standardization to satisfy the industrial thirst for regular components - Form following Function, practicality, economies of scale......
Optimization
To find the best, Fitness for purpose. State of equilibrium, performance, best achievable economy of means. Process of Optimization - Search for the best state within a model. - Biological - Architectural - Structural Optimum state is always relative to the details to which it was sought. Optimization is used in Architecture as a form finding tool.
Optimal shape of an arch - Catenary curve created by an idealized hanging chain assumes under its own weight when supported at each end.
Sidra Tree - Progressively removing the smallest amount of stressed material from a block until the remaining structure uses least material but is most structurally efficient.
Topology
The Place, the Space and everything that is in it.
Konigsberg’s seven bridges theory by relating each bank to node.
Klein surface - MĂśbius Strip - closed surface that is neither interior or exterior - cannot be fabricated without intersecting itself.
Knots - A mathematical knot is 1D though must be immersed in 2D/3D to be appreciated. Similar to how some clients struggle to read plans to a 3D model can be very helpful.
Datascapes and Multi-Dimentionality Datascape - the translation of abstract patterns. - often represents something we cannot see. - encompass a broad spectrum of design activity.
The focus is the design of environments for the interaction of their human participants. To create the environment to test our designs.
Engaging a multi-dimensional model for the process of design - this results in a fully interactive dynamic environment in space, virtual or physical.
Cellular Organisms - An interactive relationship with the place and between calls to generate emergent patterns of response that evolve across the network of individual cells.
Personal Reflection and Future Prediction
How long until we are Programming algorithms into DNA.
Designing our own systems, materiality, responsiveness and allowing a building to develop or grow allowing the scripts by which are programmed to develop its final form. Programming its cells like the Verioni pattern to react to form and function through predetermined laws.
Would this way of creating form optimize its true potential as long as the initial cells were programmed correctly.
The Datescapes would only apply to the initial functions as once the cells are released onto site they will develop dependent upon the real external environment though multi-dimensional modelling could predict possible outcomes for the form. John Johansen - Nano-architecture theories
Simulate
Analysing the priciples devised by Frei Otto and Buckminster Fuller Develop skills in digital simulation using Rhino 3D and Grasshopper. Explore principles with digital and analogue modeling.
Frei Otto Influences
Otto is a leading authority on lightweight tensile and membrane structures, and has pioneered advances in structural mathematics and civil engineering. During WW2 he spent time in a French POW camp. Here, it is believed, was the initiation of his future interest in tensile structures. Due to an urgent need for shelter within the camp Otto began experimenting with material tent material, applying his knowledge of aerodynamics to structures. Otto envisioned structures of extreme lightness as well as extreme strength, which would make the optimum use of new materials such as thin cables of high strength steel or thin membranes of synthetic fabrics. His systematic research on lightweight and adaptable construction, his understanding of the building architecture and his concern on ‘how to achieve more with less material and effort’ was to lead him towards designing some outstanding lightweight tensioned structures. ‘I have built little. But I have built many castles in the air.’
Spacial Zoning of the Structure
Tensile Structures - A tensile structure is a construction of elements carrying only tension and no compression or bending. Tensile structures are the most common type of thin-shell structures. Most tensile structures are supported by some form of compression or bending elements, such as masts compression rings or beams.
Path of horizontal forces
Development of Frei Otto’s Entrance Arch Canopy designed for the Federal Garden Exhibition in Cologne
Buckminster Fuller Influences
Buckminster Fuller’s impact on the world today can be found in his continued influence upon generations of designers, architects, scientists and artists working to create a more sustainable planet. ‘A comprehensive anticipatory design scientist’. An emerging synthesis of artist, inventor, mechanic, objective economist and evolutionary strategist. Major Themes: Synthetics - involves geometric modelling. - relates to synergy which is the behaviour of whole systems unpredicted by the behaviour or the individual parts. Dymaxion World - DY namic - MAX imum - Tens ION - dymaxion structures are those that yield the greatest possible efficiency in terms of available technology. World Game - A tool intended to facilitate a comprehensive, anticipatory, design science approach to global problems.
The Geodesic Dome - uses a sphere and thus involving the “doing more with less� principle. -Encloses the largest volume of interior space with the least amount of surface area. - More energy efficient - dec. s.f. = less exposure to hot/cold therefore less exposure to lose energy. - Concave interior creates natural airflow. - Extreme wind turbulence lessened as wind travels smoothly around the dome. - Concave interior reflects and concentrates interior energy reducing energy loss.
Experimentation
Influenced by Buckminster Fuller and Frie Otto’s work I have embarked upon an evolving collection of experiments of my own originating from their research. These consider minimal surfaces, surface tension and elements of the Buckminster Fullerine research. I intend to follow in their footsteps becoming a ‘Comprehensive anticipatory design scientist’ of the modern world.
Soap film model. Starwave Grasshopper experimentation and development of Frei Otto’s Starwave tent. Cologne
Experimentation Analogue Modelling - exploring tensile structures
Hack/ Hybridise
Choose three themes Analyse and Develop a greater understanding of these themes. Further develop skills with digital simulation. Hybridise the three themes.
Three Themes
Frei Otto - Tensile Structures - Tension - the act of stretching or the state or degree of being stretched.
Cable in state of tension between two points
Material in state of tension between multiple points
Buckminster Fuller - Dymaxion Structures - Synergetic Energy Structures - Maximum Strength - Minimal Surface
Tetrahedron - Maintains stability in chaos. - Minimum system is a tetrahedron. - Smallest mathematical structure comprising of an inside and an outside therefore is the minimum and most stable system that exists.
Development of the geodesic dome and the Buckminster Fullerine. Based upon triangulation and the Carbon 60 molecule
- Reduction in fluid pressure when a fluid flows through a constricted section of pipe. - As with a funnel - velocity of fluid inc. as cross sectional area dec.
Personal Exploration - Wind Technology Evolution - Venturi Effect - Cyclone Technology - Turbines
-Air enters system. -Angle causes it to spiral around the drum. -Air continues through conical cylinder. -Sloping walls cause air to spiral downwards at inc. speed.
Energy
Experimentation Initial Experimentation with Grasshopper - Using scripting techniques to develope a twisted tower.
Experimentation Initial Experimentation with Grasshopper forms
- Script and segment/waffle approach to fabricate digitally developed forms
Monocoque and Semi Monocoque Structures
Monocoque - is a structural approach that supports loads through an object’s external skin.
The technique may also be called structural skin or stressed skin. Spheres and Egg Shapes are examples of Monocoque Structures Showing digitally developed monocoque forms
Semi-Monocoque -
is a relatively new variation on the general concept of a stressed skin structure.
Is an extension on the Monocoque theory. The idea of the external skin supported by a sub-structure like the structure of an aeroplane or boat hull.
Showing Anologue model of semi-monocoque structure.
Semi Monocoque Internal Structure - Developed digitally - Individial straight elements that will slot together to ceate a three dimentional form.
- This is the sub structure to the semi-monocoque form allowing for a light weight , streamlined result.
Experimentation Analogue Modelling Experimentation with grasshopper lazercutting - Waffle arch structure
Experimentation - Waffle sine wave focusing to a point
Developed Semi-Monocoque Form
Turbine Theory Within The Semi-Monocoque Form
Semi-Monocoque intake uses Venturi Effect to Increase wind velocity.
Cyclone Technology into funnels (Dyson Technology) further increases velocity
Cyclone created rotates turbine Combining my research into lightweight tensile structures and wind technology I have designed a prototype for a new wind turbine.
Power Generated
Energy