Frei Otto, Bodo Rasch: Finding Form Towards an Architecture of the Minimal By Kwang Yeul Lee
Question about an architecture of the minimal : - What is ecological architecture? - How do we design and build architecture ecologically? - Why a natural architecture of the minimal is important for the future? - Why Frei Otto & Bodo Rasch research mimimal architecture? - Are Frei Otto & Bodo Rasch’s works ecological architecture? Really?
Introduction Nature is beautiful. We find an infinite variety of shapes, colours and species in it. The only imperative for living in harmony with nature is mutual respect. However, in the process of modernization we have a worldwide issue as environmental problems, especially global climate change. For instance, a temperature is being increased and sea level is being risen slightly. In spite of climbing environmental problems, we still build the unnatural buildings of past decades. Our times demand lighter, more energy-saving, more mobile and more adaptable, in short more natural buildings, without disregarding the demand for safety and security. Therefore, to solve today’s problems we need the new integrated architecture of the ecological system of the earth’s surface that is settled by man. Many people hope that the new architecture of the minimal will encourage peaceful cohabitation and make social self-regulation processes possible. The purpose of this study is to research into the definition of ecological architecture, the way of designing building ecologically and the reason that a natural architecture of the minimal is important for the future. As a result, we will study about Frei Otto and Bodo Rasch’s works, their researches and a variety of their experiments.
1. About Frei Otto & Bodo Rasch : 1.1 Frei Otto
Figure 1.1.1 Frei Otto, 1925~present th
German architect and research engineer, Frei Otto (Figure 1.1.1) has been called the Brunel of the 20 century. His work has influenced a whole generation of architects, particularly in Britain, where Rogers, Grimshaw, Cullinan, Hopkins and Jiricna all owe him a huge debt. For example, Richard Rogers’ fabric based version for the Millennium Dome (Figure 1.1.2) in London. He was born in Siegmar, Saxiny in 1925. From 1931 to 1943 he attended Schadow School in Zehlendorf, Berlin as a trainee mason. After serving as a fighter pilot in World War II, he trained at the Technical University of Berlin from 1948 to 1950. In 1957 he founded the Development Center for Lightweight Construction in Berlin. Seven years later he transferred the center's activities to the Institute for Lightweight Structures in Stuttgart. Otto exhibited a special gift for creating lightweight tent structures. In the 1950s he used models to define and test complex tensile shapes. As the scale of his projects increased, he pioneered a computer-based procedure for determining their shape and behavior. He often created pavilions composed of primary membrane elements in an additive series. He also developed a convertible roof with a variable geometry. As well as an architect, engineer and inventor, Otto also likes to think of himself as a natural scientist and experimental physicist. He is most famous for his lightweight structures. Buildings like the German Pavilion for the Montreal Expo (Figure 1.1.3) in 1967 seemed to promise a new and elegant order of architecture defined by technical ingenuity and material efficiency. His buildings offered a glimpse of how the man-made landscape might be redefined, not only aesthetically but in its sustainability. His most famous works are pavilions, Expo halls, a stadium roof, an aviary, all of which occupy privileged and experimental spaces at one remove from their cities. Moreover, he developed an alternative system of gridshell structures that followed the same principles of elegance and structural lightness. In 1960 Otto set up a biological research unit to study natural structures. Drawing inspiration from plant cells, bubbles and other organic forms, the unit developed a system of shell structures whose skins are inflated with air. Nicholas Grimshaw used this pneumatic system for the domes of the Eden Project (Figure 1.1.4). In the 1970s, Otto devised a pneumatic dome that was to span 2km over an Arctic city, but it was never built and he is now suspicious of such grandiose gestures. Otto is still active. One of his more recent projects was his work on the Japanese Pavilion at Expo 2000 (Figure 1.1.5) with a roof structure made entirely out of paper.
Figure 1.1.2 Millennium Dome, Richard Rogers, London, 2000
Figure 1.1.3 Montreal Expo, Frei Otto, 1967
Figure 1.1.4 Eden Project, Nicholas Grimshaw, UK, 2001
Figure 1.1.5 Japanese Pavilion, Frei Otto, 2000
1.2 Bodo Rasch
Figure 1.2.1 Bodo Rasch, 1943~present
Bodo Rasch (Figure 1.6) says that Otto is the only architect in Germany who does not have to try to find theoretical groundings for his constructions, but can justify them from his life. Not simply because nature’s structural principles are taken up. Rasch learned from Otto. He works with his theory, realizes in other cultures, looks for new links and experiences a spiritual component that Otto does not formulate. Rasch was born in Stuttgart in 1943. From 1964 to 1972 he studied architecture a Stuttgart University and graduated with an Engineering Diploma. Since 1997 he has been designing Islamic architecture in Saudi Arabia. (Figure 1.2.2)
(a) Figure 1.2.2 (a) Lighting for the Pizza of the Prophet’s Holy Mosque, Madinah, K.S.A (b) Convertible Umbrellas for the Courts of the Prophet’s Holy Mosque, Madinah, K.S.A
(b)
2. ecological architecture : A French artist, August Rodin said ‘Love for nature and sincerity. These are the two strong passions of genius. Everyone loves nature… Have absolute faith in her. Be assured that she is never ugly, and limit your ambition to being loyal to her…’ Early in the existence of humans, they stayed very close to nature. Their intimate and understanding relationship led to harmonious, or at least balanced, interaction. Time passed and they grew both in number and knowledge. Their attitudes changed to their surroundings, learning to protect themselves from inclement weather and enemies. As humans moved further and further away from their origins they constructed living spaces foreign to their earlier existence. Although
Figure 2.1 Fallingwater, Pennsylvania, Frank Lloyd Wright,
humans are in a part of nature, they have destroyed it to live safely and comfortably. Today, we have huge environmental damages in our world. Throughout the last one thousand years there has been a remarkable continuity of attitudes in the patterns of consumption of fossil fueil, for instance. As a result, some people argue that we should preserve our natural world to live next generation. They concern that a danger of nature is in a critical human being. Therefore, environmentally conscious design has become a major interest of architects, designers, planners, public officials and industry leaders around world. In the last years, Building development is going to be more sustainable as far as local culture and social habits of people are
1935 Figure 2.2 Soswaewon, Korea, 1520
considered. By the 1960s concern about future energy supplies was reflected in a greater interest in renewable resources, namely in the increased development of solar, wind, water power, in the use of plant and animal wastes. Particularly, Frank Lloyd Wright’s architecture had embodied the deeper ecological principles of natural building, describing design that works with natural conditions as an organic whole and a living organism (Figure 2.1). As well as most conventional eastern architecture show the organic relationships between the traditional building and nature in the aspects of environmental and social ecology. (Figure 2.2) Some of the most important ecological issues impacted by the building process are global climate change which is the result of increased pollution in the upper atmosphere, declining sources of non-renewable fuels
and increased damage
from their extraction and use. Most simply, the idea of sustainability, or ecological design, is to ensure that our actions and decisions today do not inhibit the opportunities of future generations. This means making sure that our efforts work with our Earth's ecological systems rather than in opposition to them. The impacts of human development on other natural systems continue to grow and compound themselves. Since many of the best ideas of sustainable design also help reduce waste and costs to building owners and managers, it would be foolish not to use them. Every building project requires change to ecological systems and uses energy and resources; a perfectly green building is not truly possible. Instead, every building project presents the opportunity to improve its environmental performance, within the inevitable constraints of budget and building codes. Green building is the practice of increasing the efficiency with which buildings and their sites use and harvest energy, water, and materials, and reducing building impacts on human health and the environment, through better design, construction, operation, maintenance, and removal - the complete building life cycle. Green building is also sometimes known as sustainable building or environmental building, although there are slight differences in the definitions. Sustainable building is as green building to comply with the principles of economic, social, and ecological sustainability. In contrast, environmental building is the process of addressing environmental parameters when devising plans and buildings. The practice of green building can lead to benefits including reduced operating costs by increasing productivity and using less energy and water, improved public and occupant health due to improved indoor air quality, and reduced environmental impacts by, for example, lessening storm water runoff and the heat island effect. The focus of green design is for the project to work in harmony with the natural features and resources surrounding the site, and to use materials that are sustainably grown or recycled rather than new materials from non-renewable resources. Green design often emphasizes taking advantage of renewable resources, e.g., using sunlight through passive solar, active solar, and photovoltaic techniques and using plants and trees through green roofs, rain gardens, and for reduction of rainwater run-off. Many other techniques, such as using packed gravel for parking lots instead of concrete or asphalt to enhance
replenishment of ground water, are used as well. Overall, the role of architects is important to specialize in sustainable solutions based on solar design and best practice in health, materials and resource consciousness for buildings, cities and communities.
3. Light Structures : Throughout the history of architecture, especially early on, great interest has been taken in the models for structure that nature offers. At the end of the twentieth century, technological advances and research by some architects and engineers has made it possible to build lighter structures on the same bases as those of the natural world. One of the greatest achievements in the fields of architecture and engineering is in the development of lightweight structures. The development of new lightweight materials has led to revolutionary changes in the world around us. Take the tremendous advance of polymers over the past forty years. Their potential applications today are almost numberless : from dairy product packaging to car components, and from carpets to pipelines. Technological developments now enable complete car Figure 3.1 Branched constructions, Frei Otto
dashboards to be manufactured from one and the same material. This makes the recycling process far simpler and more energy-efficient.
Scientists have studied light stable structures such as bones, insect and mollusk shells, skins and larger shells. The story of ‘Lightness’ is not just about airplanes, or composite materials, although they play an important role. It really deals with the building structure of all things made and grown. The skeleton of a dinosaur, for example, inspired Frei Otto to build a crane. The technique looks for constructional models based on light, stable structures. In biology, Otto found a fertile field of research for seeking resistant and rational structure. He is the world’s leading authority on lightweight tensile and membrane structures, and has pioneered advances in structural mathematics and civil engineering. For this reason, he founded the famous Institute for Lightweight Structures at the University of Stuttgart in 1964 and headed the institute till his retirement as university professor. Frei Otto is concerned with the fundamentals of structure. In pursuing the age-old question of all construction – how to achieve more with less, that is, less material and effort – he has elevated the traditional tent to a modern building type capable of remarkably large spans. Otto believes in modern technology, and, from the beginning, envisioned structures of extreme lightness as well as extreme strength, which were to make optimum use of new materials such as thin cables of high-strength steel or thin membranes of synthetic fabric.
4. Forms originate in all natural spheres : From the earliest days of human civilization, man has taken inspiration and design guidance from structures found in nature. We can use to create our own structures from many of shapes and forms in the natural world. ‘Structure in nature suggests that there must be some fundamental principles and laws, an intrinsic force system, which can form the basis for the design of minimum diversity building systems’, says Peter Pearce in his book ‘Structure in nature is a strategy for design’. There is mutual understanding between biology and technology. Nature is as role model to improve our architectural environment. Consequently, Frei Otto and Bodo Rasch specialize in forms originate in all natural spheres as four categories such as inanimate nature, animate nature, animal and human technologies, and used by man. 4.1 Self-formation Processes in inanimate nature : All material objects in nature and technology have form and put together, thus they are constructions. Natural objects are natural constructions. They consist of parts and elements and come into being as a result of self-formation processes. Furthermore, they are formed by processes, and these can be recognized from of the objects. Many processes and their products are independent of the material, incidentally. Often the same produce similar objects. For example, whatever material heavenly bodies are made of, they always become spherical with increasing size.
(a) (b) (c) (d) (e) Figure 4.1 (a) Heavenly bodies Liquid balls, (b) Contraction strain cracks, (c) Surface decoration Crystal formation on surfaces, (d) Rock arch, (e) Rock tower
4.2 Animate nature : Animate nature uses a lot of inanimate nature’s self-formation processes like the formation of small bubbles, threads and patterns, but it differs fundamentally from inanimate nature in that her objects die and ultimately become dead natural objects. Animate Objects reproduce by division and sexual multiplication.
(a) (b) (c) (d) Figure 4.2 (a) Reproductive multiplication cell division, (b) Berries, (c) Ramification, (d) Human foetus, (e) Leaves
(e)
4.3 Animal and human technologies : Highly developed and mobile animals have been using technologies for shaping products. In the animal, fantastic structures help us to understand the basics of structural concept, which is, without doubt, the backbone of the creative constructive design within our architecture. Therefore, techniques used by insects and spiders, whose forms and constructions are anchored genetically, are old in terms of biological development.
(a) (b) (c) Figure 4.3 (a) Wasps’ nest, (b) Spiders’ webs, (c) Suspension Bridge, (d) Fishing nets
(d)
4.4 Self-formation Processes Used by man : Today there is such a thing as made-up nature. Man can strive to shape nature in the image of a nature he has made up himself. When objects form of their own accord man can make direct use of the process. Moreover, there is a new form of self-formation process, using computer optimization programmes to find solutions for practical problems.
(a) (b) (c) (d) (e) Figure 4.4 (a) Fold formation in crumbled foil, (b) Suspended chains, (c) Self-formation in well-building, (d) Soap film, (e) An explanation of spatial networks
5. Frei Otto & Bodo Rasch’s Experiments and Works Frei Otto developed models and methods in which forms generate themselves in order to observe and analyse the processes by which material objects originate in all realms of nature, technology and architecture. In the first stage, Otto observes the forms he finds in nature, which in their origin and efficacy are even more relevant to his researches. Most of the shapes employed in shell and membrane structures, such as hyperbolic paraboloids, seem without precedent in modern architecture, which has always aimed at a reduction to elementary geometric forms. Additionally, he regularly holds seminars at which biologists discuss their research on plant and animal structures. Besides such obvious adaptations as the vertebrae column, his methods themselves have a tendency to produce forms which, for example in the tree structures or space frames, are of outstandingly organic character. To addition, Otto specializes in tensile structure and biological research. The nature of most construction materials involves only compression forces and the concomitant bending and bucking moments, it is insignificant in conventional buildings. The reverse is the case with tensile structures where only a few members, such as masts, are under compression while all others, for instance, cables and membranes, are under tension. In order to introduce tension and to ensure rigidity, membranes must have specific shapes, which in most cases are based on anticlastic or saddle-like curvatures. Furthermore, these curvatures can, if correctly determined, generate the smallest possible surfaces within given curvilinear boundaries. Otto’s experiments with soap films and bubbles have shown that self-generating and self-optimising forms in tents, cable net structures of all types, various membranes and air or water-filled pneumatics have been proven in engineering and are gaining increasing application. An enormous range of experiments were carried out by him. However, here only some of the models and experimental equipment are described that is used as form-finding methods in architectural design. Moreover, some of his works are introduced and analysed in order to show how to relate to his experiments. And also our architectural experiments at University of East London with VBA (Visual Basic Application) AutoCAD are demonstrated.
5.1 Soap film Experiments for Producing Minimal Surfaces : Soap film experiments to produce minimal areas as form-finding models for tension-loaded membrane and ropenetwork constructions. The Belgian physicist Joseph A.F Plateau (1801-1883) made soap bubbles the subject of experimental observations and scientific study. He immersed wire loops of various shapes in a soap solution and was able to find a minimal surface for each given boundary because the soap film will always form a minimal surface due to its surface tension. A soap film regularly contracts to the smallest surface possible. It then takes up the form of the minimal surface, which is clearly defined mathematically. This minimal surface, as tension equilibrium form is the ideal basis for building the most efficient lightweight tension membrane structures with a minimum of mass and materials. Membranes made up of liquids, known as “soap films”, form when a closed frame is dipped into membrane-forming liquids and then taken out again. The frames can be made of thin wire or threads. The best-known membrane-forming liquid is soap lye. Very thin membranes are produced from distilled water with a few drops of detergent or “Pustefix” bubble fluid. Liquid membranes are prestressed, flexurally non-rigid and plane load-bearing constructions that are nevertheless tension loaded. The forms produced in the experiments can provide extremely precise models for the tent constructions and be constructed as design and working models in the widest possible range of materials and used for further processing within the design process. (Figure 5.1.1, 5.1.2) The tent is one of the oldest artifacts which is still useful in the modern world; it is one of the most ingenious shelters humans have produced. Today, nomadic tribes use tents extensively in areas where natural shelters are scarce, such as the tundra, desert, prairie, unobstructed space and flat terrain. Frei Otto experimented at a very early stage when formfinding for membranes and nets for tent-like constructions with different membrane tensions. For this he used nets made of springs and rubber springs. He was the first to examine the link between form and structure and thus discovered the significance of the self-forming minimal surface for the design and shape of tent structures. He also experimented rope net constructions which are subject to the same laws as membrane tent constructions, but they can cover considerably larger spans. A beautiful example of a membrane, made of a metal cable structure filled up with transparent polycarbonate tiles, is the roof the Olympic Stadium in Munich. (Figure 5.1.3, 5.1.4)
Figure 5.1.1 Soap film model, Starwave
Figure 5.1.3 The large measurement model for the stadium roof in Munich
Figure 5.1.2 Starwave tent, Cologne, Frei Otto
Figure 5.1.4 Olympic roofs, Munich, 1972
- Design Methodology : Initial design ideas are first sketched out freehand, as consideration is given to the purpose of the structure; a variety of different concepts might be established that would all be developed in parallel. Initial scheme design drawings are prepared using CAD, for new ideas can quickly be tried out, and conflicts shown. Fist attempts can then be made at form finding, using either sophisticated computer programmes to iteratively solve the geometry matrix for uniform stress, or by photographing soap-film models that naturally take up the shape of minimal surface. The geometry found is incorporated into the CAD drawings from which cutting patterns are prepared and small-scale models produced.
(a) (b) (c) Figure 5.1.5 (a) Soap film model, tent with bow, (b) Form finding of the membrane with CAD, (c) Computer rendering of the tent structure, SL-Rasch
- Numerical Analysis in the Design Process of Lightweight Structures : Minimal surface structures are double curved at any given point of their surface. The surface’s curvatures can be synclinal or anticlinal, defining tangential planes towards the corners. The complex geometry and the architectural appearance of these double curved structures as well as their covered spaces can only be studied in three-dimensional models. Frei Otto said “I always tried to think three dimensionally. The interior eye of the brain should be not flat but three dimensional so that everything is an object in space. We are not living in a two-dimensional world.” And – even more so with regards to the structural analysis and the manufacturing of these structures – it requires very precise 3Dmodels, which are nowadays mostly numerically generated by the computer, using particular software. In order to achieve the highest quality results the entire design process is developed in a complementary process, through the combination of CAD linked finite element software and computational fluid dynamics software. This software uses algorithms that mathematically describe tension equilibrium elements, to generate and to simulate minimal surfaces within defined boundary conditions. This software generates numerical soap films as real tension equilibrium surfaces. The computer model allows fast modification and comparison of different shapes and thereby supports the architectural design process.
Figure 5.1.6 Numerical analysis in the design process, SL-Rasch
Figure 5.1.8 AutoCAD drawing, SL-Rasch
Figure 5.1.7 Prototype as a ‘minimal shaped’ tension equilibrium form, SL-Rasch
- VBA AutoCAD Experiments : We can write a little program in Visual Basic for Application in AutoCAD. Therefore, we can just tell the application to draw a line and collect the information in a data structure. Computing shapes and structures as outcomes of simple repeated instructions called algorithms has become very fashionable. That is because algorithms can produce complex looking patterns quickly with little effort. Using the sinusoidal curve to delineate the path of the delimiting body, we can be building up wall-like sequences via surfaces or series of faces. Such experiments show to create space or surfaces supposed to be a horizontal shelter as roof. Below, we can see some results of experiment with scripting in VBA AutoCAD as faรงade similar to tent structure.
Figure 5.1.9 AutoCAD drawing as faรงade with scripting in VBA AutoCAD, UEL
Figure 5.1.10 Neural Network : Self-Organizing Feature Map, VBA AutoCAD, UEL
5.2 Simple Experimental Apparatus to create the Form of Pneumatic Construction : In nature a great many forms are made up of micro-spheres, pneumatic structures. The micro-sphere behaves like a soap bubble in water, with a consistently flexible and resistant layer around a watery or gaseous content. Every animal or plant cell is a pneumatic structure made up of membranes and contents – the protoplasm. One of the fundamental properties of liquids is surface tension, the strength of which gives shape to typical soap bubbles. When the bubble presents minimal surface, its shape results from a minimal amount of material. Besides being resistant, these light, flexible structures attain great plasticity. The use of air as a structural material is, therefore, not new. In everyday life there are pneumatic structures in which air inside a resistant, protective shell-like covering supports a heavy weight. Such is the case of vehicle tyres, air mattresses, inflatable toys, sails inflated by wind, balloons, balls, and so on. It is no accident that the forms of pneumatic constructions developed by humans resemble natural shapes. Over the past three decades, air has become recognized as an important component of many structures. The apparatus for inflating clear transparent pneumatic constructions is a valuable aid, especially when finding forms for air-supported membrane halls. In this experiment a thin sheet of PVC or acrylic glass is heated and inflated with compressed air. Experiments with plastic-stiffened rubber films are also suitable for finding form pneumatic constructions. In this case rubber sheeting is used. It is inflated and placed on the glass fabric soaked in liquid polyester. Another method uses rubber films coated with liquid plaster. Further tests with larger air-supported models, static-dynamic calculations, wind tunnel experiments and others are necessary before an air hall is finally built. This model-building method is particularly suited for reaching a shape for air halls which are called pneumatic constructions in architecture and water-filled membrane constructions.
Figure 5.2.1 Soap bubbles, foam structure
Figure 5.2.2 Exhibition pavilion at the 1964 World Fair, New York
Figure 5.2.3 Shape study for an air hall with internal drainage
Figure 5.2.4 “City in Antarctica” project study, 1971
5.3 Experiment with Suspended Chains to find Shapes for Suspended Constructions : Frei Otto realized early on that the principles that determined the forms of suspended chain nets also applied to grid shell structures. Dependent only on the net pattern and configuration of its attachment, the hanging form generates itself by bringing its own weight into equilibrium. The uniform square mesh of the nets produces shells with the required continuous grid lines and equal distances between the connecting joints. In perfecting this model technique, Otto developed a tool for determining empirically, the forms of grid shells for any possible plan configuration. Suspended find chains in a model precisely reproduce the form of ropes or wires suspended in the same way, in high voltage cables, for example. A dense pattern of suspended chains gives the shape for suspended roofs that are stabilized by their own weight without pre - tension. Roofs of this kind are now found in large numbers all over the world. Chain models reflect the arches and vaults that can be built with them as a model. Chain networks showing significantly more complex forms than freely suspended individual chains can be constructed from small pieces of chain or short bars fastened together flexibly. A suspended structure can be stabilized by sufficient self-weight, by stiffening the roof surface, or by guying. Especially, the pagoda and temple roofs of the Far East are made of freely suspended nets. (Figure 5.3.1, 5.3.2) One of Otto’s major achievements, this large hall is the culmination of his grid shell research and demonstrates the feasibility and economy of these compression structures at any scale. However, the simplicity of the concept can be misleading, as the size – no less than 34,000 bolts were required to connect the 72km of laths - requires calculations of such complexity that they cannot be done without computers. (Figure 5.3.4)
Figure 5.3.1 Suspended model using a squre-mesh chain
Figure 5.3.3 Design model in wire fabric
Figure 5.3.2 Busok Temple, Korea, 676
Figure 5.3.4 Mannheim lattice shell, 1972
5.4 Experiments for the Investigation of Optimized Path Systems and Branched Constructions : The minimal path system is ideal for traffic routes such as footpaths, cycle tracks, roads, railways and motorways and a special experimental arrangement has been devised to investigate it. This very simple experimental procedure is also suitable for investigating power transport systems especially in lattice constructions made of compression, and bending,loaded slender bars. Branched constructions are three-dimensional supporting systems used increasingly in steel, wood and concrete building. Umbrella structure can be presumed that the umbrella is the oldest type of convertible and very useful roof construction with a small span. It is an archetype, related in form and structure to the yurt and the tepee.
Figure 5.4.1 Two-dimensional thread model
Figure 5.4.2 Branched constructions
- VBA AutoCAD Experiments : We can write a little program of agents in VBA AutoCAD as tree structures similar to Resnick’s experiment in ‘Termites, Turtles and Traffic Jams’. Agents are essentially short algorithms that contain a set of rules, which describe reactions to situations they encounter. First the agent starts toward north on the screen. The agent draw the trunk of the tree, then “clone”, a new agent, one heading 45 degrees to the right and new one heading 45 degrees to the left. That is all for the initial agent. Below, there are a basic idea of the tree structures and several interesting results of the agent. Mitchel Resnick said “the tree has become a symbol of Logo recursion. We can think of a tree as a trunk supporting two smaller trees, each of which is a trunk supporting two smaller trees, and so on.”
Figure 5.4.3 The concept of agent as tree structure
Figure 5.4.4 Recursive tree-drawing sequence, Richard Dawkins
(a)
(b)
(c)
(d)
(e)
Figure 5.4.5 There are different inputs of angles such as (a) 15, (b) 30, (c) 60, (d) 90, (e) 135 degree, A variety of tree patterns, VBA AutoCAD
To conclude : Frei Otto is concerned with the serious architectural environment. Through his experiments and works, he developed his new concepts by focusing his investigations on one of the principal forces extant in all structural systems from the minimal in nature. He believes in modern technology envisioned structures of extreme lightness as well as extreme strength. Because our times demand lighter, more energy-saving, more mobile and more adaptable, in today’s buildings. He insists to solve today’s problems we need the new integrated architecture of the ecological system of the earth’s surface that is settled by man. Overall, we believe that many students and professionals in an architecture are demanded to understand between nature and a ecological architecture through researching the minimal in nature in order to improve our health and nature.
References : - Frei Otto, Bodo Rasch : Finding Form : Towards an Architecture of the Minimal : Edition Axel Menges, 1995 - Ecologic Architecture, Richard L. Crowther, 1992 - Bio-Architecture, Javier Senosiain, 2003 - The Ecology of Architecture, A Complete Guide to Creating the Environmentally Conscious Building, Laura C. Zeiher, 1996 - A Study on the Characteristics of Ecological Architectural Space of Frei Otto, Gyoung-Sil. Choi, 1997 - Lightness, The inevitable renaissance of minimum energy structures, Adriaan Beukers & Ed van Hinte,1999 - IL 17, The work of Frei Otto and his teams 1955-1976, Ludwig Glaeser, 1978 - IL 18, Seifenblasen Forming Bubbles, Klaus Bach & Berthold Burkhardt & Frei Otto, 1987 - Turtles, Termites, and Traffic Jams, Explorations in Massively Parallel Microworlds, Mitchel Resnick, 1997 - The Evolution of Evolvability, Richard Dawkins - SL-RASCH Special and Lightweight Structures, http://www.sl-rasch.de/ - ARCHITEKTURMUSEUM TU MUNCHEN, http://www.freiotto-architekturmuseum.de/ - WIKIPEDIA, http://en.wikipedia.org/wiki/Frei_Otto