The Fuller’s heritage: organic models and artificial microcosm in XX century domes.

Michela Rossi1

Abstract: The dome derives from the arc, developing structural principles of heavy masonry.

Buckminster Fuller has developed a quite new design concept to construct light domes improving his “tensegretic structures”. Geodesic domes adopted the spatial symmetries of regular solids, and were inspired by the analysis of the self-balance of cell membrane. Fuller carefully explained that they developed a principle of nature, without copying it as the objects and procedures copying the biological principles cannot be licensed by the law. The study of self-sustaining equilibrium of closed systems and the imitation of cellular energy balance allowed Fuller to turn the dome, born as masonry building, into a light construction. Later on, other architects took back the light dome from different structural principles. All of them evoke organic models reinterpreting the surface membrane, borrowing something from Fuller and yet again reinterpreting his design but not copying him

Kaywords: nature models, light domes, symmetries

1. THE NATURE AS A MODEL. INTRODUCTION The relationship between nature and design has become more intense in the past years, and it has ever been a constant source of inspiration; its models still inspire a wide range of concepts and the human building process and creation. The origin of this interest in the shapes of nature kingdoms is unknown but explicit, thus both living beings and inanimate structures show structural and aesthetic solutions in their wonderful objects. It is also well documented by Art and Architecture treatises, after Vitruvius tale about the birth of the classic order and its relations to human body. His statements were the source of later work by authors of the Renaissance, still pursuing the role of beauty in geometry from subtle imitation of natural law of proportion expressed by Golden ratio, up to Gottfried Semper and Owen Jones, explaining its regular conformations as ornament model for surface decoration. The historical point of view is important to understand contemporary architecture. Semper rethought architectural buildings in terms of textile and materials. While Ruskin and Pugin recognised the surface as the opposition between ornament and building, he studied how geometry and matter can work together in the textile drawings on the surface. Many decorative patterns show a clear phytomorphic inspiration, as everybody can see in the ornamental drawing of historical architecture and artifacts. Several moldings of the classic order stylize organic forms, but the maximum stylization of nature is expressed by arabesque, using geometry instead of analogical shapes to represent the Creation.

                                                                                                               1 Michela Rossi, Politecnico di Milano, Italy, michela.rossi@polimi.it

The ornamental drawing expresses a suggestive sample of the relation between nature and its interpretation in design. The surface decoration is only one aspect – perhaps the most visible - of the issue that reveals more complex dealings concerning building structures. According to Vitrivius only the integration of firmitas, utilitas and venustas gives concinnitas and ornament play its true role together with the building as a part of it, in architecture and in everyday objects. As a part of the whole, the ornament can express the building concept, which is a priority topic. Before addressing the issue of ornaments, design questions effect a range of static and mechanical problems too. Therefore the concept of structure is the cause, and ornament is the effect of design choice.

Figure 1 – Formal relationships between architecture and nature in students’ drawings. Nature was the only available model when Man started imitating it, and the development of science and thought – on empirical observation and logical construction – is deep under-woven with building skills and formal concept of Architecture shape. In the same way it is strong tied with the scientific knowledge of the world we live in, that man explored and explained from the wider universe of cosmos to the smallest organic cell, by similar models. Through the centuries these were based on Geometry. With time they started referring to other branches of Mathematics that were more incline to numbers, functions and algorithms to shapes. The effect of this ‘widening’ is a change in the formal

concept of the model, not the significance of the model itself which is why Geometry is directly connected with maquette building whereas mathematical representation opens up to virtual modeling. The representation tools are important but they do not shape the design solution, al least not absolutely, and nature ever offers proper solutions to new questions of designers. This happens, as previously, on two different levels: as aesthetical suggestion and as application of scientific knowledge. The Mathematics play the same game with their models, developed to explain the world. About design they are both interesting. Critical essay showed many sample of organic design, focusing just on formal inspiration. Two exhibitions were significant: Art and Nature edited by P. Portuguese in Rome in 1998 (2), and Nature Design at the Museum für Gestaltung in Zurich in 2007 (9). The first one was focused on the evidence of a common configuration with geometric rules and regular symmetry, dealing mainly with historic architecture, but a few famous samples from last century. The immediate comparison of likeness underlined formal concepts, but actually most of the samples evoked nature, rather than its inspiration in architecture.

Figure 2 – Plane and spatial lattices in Keplero’s drawings (Harmonices Mundi, 1619).

The other exhibition showed the changing attention, since the beginning of XVIII century, remarking as the main interest moved from shape symmetries to dynamic processes, blowing in the ’90, with the intensification of the relation between nature and design. A new attention to organic processes characterizes several innovative works. The exhibition editor states that it “is intended to show the multiple possibilities in the rediscovery and reinvention of nature, and to open new perspective” to design, while biotechnologies act on the systems of nature, changing its very constructions. Architecture history shows several cases in which nature models stimulated real design innovation, that mainly means technical invention about structures, materials or building processes.

The most famous is just the formal articulation of the classic order, but we are able to list genius dealing with organic models to solve design problems. First of all Leonardo, who studied birds' wings– among other anatomical issues - to develop flying machines, and Kepler, fascinated from the beauty of nature conformation, who studied lattices and plane tessellations starting from the regular geometry of beehives. The Linne’s systemization of nature in a quite new Systema Naturae, that ruled all living beings depending on their evidence and morphology, and Darwin’s Theory of Evolution, based on the variation within the species of different organisms from common ancestry, developed a strong interest toward biological organization of natural shapes. The new science of morphology, just based on the renowned importance of shape on life, firsts portrayed and ruled the great variety of nature forms, pointing up the beauty of its regular conformations. Goethe’s work as a morphologist stresses the wide interest of his time to shape problems that culminate in the research of the reasons of form.

Figure 3 – Tables from Ernst Haeckel’s Kunstformen der Nature.

Scientists were fascinated by shapes as they conceived as a distinctive but rather selective type of character, and naturalist’s work had a great influence on arts, starting with the tables of Haeckel’s Kunstformen der Natur (3). The same attention joins the different interpretation of Ruskin and Van de

Velde, up to Art Nuveau that celebrated the dynamics of plant growth. After the formal severity of the Enlightenment, the XIX century was affected by rich ornaments and, following the interest of science, liked organic forms of flowers and plants. Semper and Viollet le Duc admired the organic harmony of nature, which produces a great variation of organisms through the repetition of few basic form and elements. The adherence to the nature laws does not mean a mindless repetition but a model of coherence in design processes. Quoting his master Semper, around 1907 Berlage (1) stated that evolution is based on a few forms and types, alluding to the work of Haeckel, who since the 80’s estimated the existence of more than 4.000 species of Radiolaria, without any evidence of limitations from habitat. A few years later, D’Arcy Thompson (4) explained the dynamic of living organisms the transformation of their ‘shape’ through growth and movement. Engineers’ inventions have less evidence, as those inspired from the skeleton of the mammals that became an important model in structure and machine design. A fitting example is found in the Kulmann crane, that copies the shape of the thighbone head. The application of formal property of nature objects helped several innovative solutions, as shell structures and stressed membranes. The approach to organic design changed radically trough the XX century. Under the influence of Expressionism poetry we can recognize two branches of tradition. Some artists, such as Gaudì, Baldessari, Michelucci, Aalto, Saarinen, Mirò and so on, conceived nature complementary to design and imitated in their growing works the continuity of nature, avoiding figurative ornaments, while Fuller and Frei Otto conceived design as strictly under woven to nature. They imitated the organic shape in the concept of structures. Process and function became the central factors of design. Fuller applied the organic properties of cells and fabric to building art, and patented the tensegretic structures and the geodesic domes, while Otto’s work applied to membranes the development of fabric concept, with self contained entities based in a modular system, in which details correspond to the whole. Frei Otto studied how soft materials find their own form with analogical models of tensile structures and in the earlier 90s developed in Munich Olimpia Stadium “optimized path sistems, with experimentation similar to that used by Gaudì for the Sagrada Familia”, by the application of minimum surface balance in soap bubble, drops and foam (11, p. 352). 2. THE SHAPE AS THE ANSWER. FULLER’S DESIGN RESEARCH

The key historical figure of organic design was just Buckminster Fuller: "The greatest of all the faculties is the ability of the imagination to formulate conceptually. Conceptuality is subjective; realization is objective. Conceptuality is metaphysical and weightless; reality is physical. The artist was right all the time. Nature is conceptual" (5).

Figure 4 – Filling the space with lattices: tetrahedron, octahedron and cube-octahedron and light structures layout.

Actually, with Fuller’s work, the history of organic design become a function of building efficiency. He developed organic processes for mobile architecture that functioned as self-supporting systems of tensegrity structures, later developed in geodesic domes that deal with the balance of forces. Geodesic domes are huge light spheres, and at first glance they do not remind natural forms, but they apply the study of cell equilibrium in a balanced system of vectors on spherical surface. “We have relationships - but not space... "Synergy" means behavior of whole systems unpredicted by the behavior of their parts taken separately ... It is dealing with the whole that makes it possible to discover the parts". The invention of geodesic domes was successful applied to military utilities, such as in temporary architecture. After the II World War, they had a large civil use and dominated with the USA pavilion being a light dome several world exhibitions. Through the Cold War, they became the symbol of the western technical predominance. Finally the Fuller’s domes stressed a technological futuristic vision. He suggested mega structures able to cover whole cities. The research about light structures derives from the enforcement of the morphological studies of scientists as D'Arcy W. Thompson, who stated that nature follows the law of gravity but in its smallest reality pursuits the balance of forces on the cells surface and explained the variety of shape of nature and cosmos as a great efficiency game: "There is no shape of the Universe. There is only Omni directional, non-conceptual "out" and the specifically directional, conceptual "in."

Figure 5 – Lattice and fabric on plane and spherical surfaces, the stress balance in triangular patterns.

Fuller begun his research following D’Arcy Tompson’s statements on cells behavior and geometry Radiolaria, that shows all the Plato’s regular solids, that do exist in crystals but dodecahedron, due to chemical relations. The starting point was the tetrahedron, the first of Plato’s solid, because it is the simplest system in Universe, and the minimum set between macrocosm and microcosm. The study of this very simple shape led him to reason on the filling of the space by the packaging of spheres, that produces a lattice of octahedron and octahedron. He supposed that attributes of the tetrahedron provide a powerful conceptual model to light structure, conceiving regular polyhedron as the it as the basic "building blocks" of nature, in both physical and meta-physical universe, just as Plato did when stated that the tetrahedron, octahedron, hexahedron (the cube) and icosahedrons represented the four elements. He meant the tetrahedron as the simplest form of every package, and the vector model of quantum, matching together two negative and positive halves of quantum. As he stated later in his Synergetic Geometry (6), “...we find that a geometry of configuration emerges from our awareness of the minimum considered components. A minimum constellation emerges from

our preoccupation with getting rid of the irrelevancies. The geometry appears out of pure conceptuality. We dismiss the irrelevancies. The geometry appears out of pure conceptuality. We dismiss the irrelevancies in the search for understanding, and we finally come down to the minimum set that may form a system to divide Universe into macrocosm and microcosm, which is a set of four items of consideration. The minimum consideration is a four-star affair that is tetrahedral. Between the four stars that form the vertexes of the tetrahedron, which is the simplest system in Universe, there are six edges that constitute all the possible relationships between those four stars. The tetrahedron occurs conceptually independent of events and independent of relative size. By tetrahedron, we mean the minimum thinkable set that would subdivide the Universe and have the interconnectedness where it comes back upon itself...The basic structural unit of physical Universe quantation, tetrahedron has the fundamental prime number oneness.” Whilst working on the polyhedron symmetry he studied the vector equilibrium on the surface of the sphere, convinced that it provided the possibility to base designs and architectures on those models that nature employs (5). He bethought nature systems as a lesson for humanity's success through the study and application of the recently discovered cosmic architecture to the problems confronting humankind. From this utopian point of view, he spent however a great deal of attention on demonstrating that his structures were invention only inspired by nature systems because international law don’t allow that natural processes be patented! (7) Working on models, he found that cube-octahedron had the same structural sternness than octahedron and it has the unique property that the ray of the circumscriber sphere was equal to the side. He called this solid Dymaxion, contraction of "dynamic maximum tension", and since 1928 the word became the brand of several inventions related to what he meant as 4D architecture: the Dymaxion house (1920), the Dymaxion car (1930), Dymaxion bathroom (1930) and the Dymaxion World Map (1946). The last one was a determinant step to geodesic domes because the map was a flat stereographical projection of earth on a cube-octahedron, and thus it allowed minimum deformation on the edges, with shorter routes for air navigation. In 1954 the Fuller Projection Map was adapted to the icosahedrons, which has more faces and thus allows minor deformation along the regular lattice of draw lanes on the 60’s edges. After Fuller, all other flat world maps contain some distortion either in shape, area, distance or direction measurements, and fail to highlight the patterns and relationships emerging from the process of globalization, only his projection allowed the perception of relation between the earth and its inhabitants. Geodesic domes adopt the stereographic projection to draw on the sphere a lattice shell structure based on great circles, that intersect themselves in triangular elements in isostatic balance. The structural concept came from tensegrity, the term that Fuller coined as a contraction of tensional integrity, referred to very light structures with isolated compressed elements inside a net of continuous stressed wires. The compressed bars do not touch each other and the pressed tensioned cables delineate spatially the system. In the simplest tensegrity structure, each of three compression members is symmetric with the other two, and symmetric from end to end; each end is connected to three cables which provide compression and which define the position of that end, but due to their concept tensegretic structures are open and cannot enclose a room, as domes do. Final surface is a mesh of triangles defined by stereographic projection. If this is done exactly, each sub-triangle edge is a slightly different length, and to minimize differences their vertices can be moved, with triangles with lying only approximately on the sphere: building efficiency is more important than the geometrical perfection of the concept. Fuller’s stadium on vectors balance was later collected in the two volumes treatise Synergetic, that was dedicated to H.S.M. Coxeter as a master of geometry and would have had pictures by M.C. Escher, who applied his artistic research on room lattices too, studying central symmetries starting from crystals. The mathematician A.L. Loeb wrote in the preface that the book marked a significant revival of interest in geometrics as science of configuration, banished in the Age of Reason as a superstition while Fuller searched “for a natural and truly rational coordinate system eventually led to the tensegrity concept and the construction of geodesic domes”. Following the interest in configuration, in a rather short time it would increase the attention to nature, whenever from different points of view. Some architects designed light domes and building with a kinetik architectural skin. None of them apply the geodesic principles, but they saved Fuller’s heritage in a quite different development of the organic concept. Among them, there are Norman Foster, the

two Italians Renzo Piano and Massimiliano Fuksas, and the younger Lars Spuybroek.

Figure 6 – Geometry and Symmetry in nature architecture in Berlage and Frei Otto’s studies of modular tense structures.

3. THE ORGANIC MODEL AS DESIGN INSPIRATION.

During the last half century, Fuller was not the one who built light domes. In 1949 Paolo Soleri (1917), a learner of F.L. Wright in Taliesin, had his first commission and with M. Mills experimented a opening dome on the main room of the Dome House. On a flat stone and concrete basement that seem to grow from the ground, it has a light opening dome, with 16 aluminum ribs on the meridians, and horizontal partition under a constant angle. A double shell allows it to open by turning. The building concept joins the weight of the earth and the light of the air and signs Soleri’s original interest to underground architecture and mega-structures. In Arcosanti, since the 70’s he will develop his urban utopia based on the concept of Arcology, meaning just architecture coherent with ecology, with concrete underground domes and lighthouses facades. Also Renzo Piano pursues a sustainable architecture, and he states that designers should understand nature to build a respectful and intelligent contact with the environment, but his relationship with nature is less utopian. He conceives architecture as a second nature overlapped to the true one, and he addresses his main attention to the energetic behavior of the building, by capturing solar energy and studying shadows and ventilation. Like Fuller, Piano work about structures of sailing in light building with a transparent skin on an iron skeleton and organic concept but he denies is any emulation. Actually, he mains that the observation of the nature teaches a lot about physical and mechanical laws, but analogies in design are reference more than copies, because imitation is naive (10).

Figure 7 – Renzo Piano’s boubles in Turin and Genoa (students’ 3D models). About the beginning of the millennium he designed two light domes in Italy: the Biosphere in Genoa, and the Lingotto Bubble in Turin. The first is like a floating sphere, going out of the water with its main part. The second is suspended on the roof of the building and it reminds the shape of a sea urchin. Despite a different shape, they show similar structure and they can be compared with Fuller’s. The two domes have a quite different geometric concept: unlike Fuller’s, they have not any geodesic structure, but a geographic lattice of meridians and parallels, drawing a window-frame of spherical quadrilaterals. The shells have 16 bearing ribs (32 segments), with 9 parallels in the Biosphere (on 1 of the vertical diameter) and 12 in the Bubble; the great circle is respectively between the second and the third and on the third parallel from the bottom (on the great circle) and in both of them and on the top there are only 4 spherical triangles. The Piano’s design allows a regular drawing around the vertical axe, but the Biosphere requires ticker steel frame and two sets of bracing wires, that draw 16 loxodromic spirals on the inner side, with constant angle to the pole as in compass navigation.  

Figure 8 – Spherical lattices in Piano’s Biospheres in Genoa and San Francisco.

A set of domes covered by a grass roof with nine green hills characterizes the inner room of the new building of Science Academy in San Francisco, designed by Piano in 2008 as the most sustainable museum of the world. The inner domes host the Biosphere with a Rainforest in a controlled atmosphere, the Planetarium and the entrance of the Aquarium. The spherical shape recalls to that of the earth. These spheres has 16 ribs as previous and 11 parallels, with an angle of 10°, as the 12th segment on the pole. This way, the dome appears less height on the ground as the Turin bubble, but without deforming the geometry of the sphere. The elevation of the two spheres differs slightly, but the plan has the same symmetry. The surface lattice do not came from the shape properties as Fuller’s, but from the drawing of plane sections and the structure has its own relation with the shape geometry, similar to that of earth representation. Fuksas is a theoretic of architecture symbiotic with life and express his principles by transparent wraps with organic shape that are not just domes, but are however light structures with organic inspiration. He designed two ellipsoidal bubbles for Nardini Distilleries (2004). These recall the shape of a still elevated on its tripod. The whole building, partly raised and partly underground, is designed to fit into the environment without requiring any trees to be cut down or any reduction in green space, with a respectable relation. The design pursuits a checked energy waste, but it doesn’t care too much about the structural efficiency of centering, drawing a lozenges pattern on the light surface. The two structures are made of 360 pieces of laminated glass curved in two directions, sustained by a double set of elliptic rings on vertical planes. The construction required skilled labor, mainly because every single piece making up the elliptical form is unique.

Figure 9 – The “stretch” pattern of the of Milan Trade Fair around the hole pillars. The Milan Trade Fair (2005) has a monumental roof. It is conceived as a light skin. It envelops the bottom of the squared exhibition sheds, which are aligned on a mile-long central path. The exhibition fairground is then covered by an undulating transparent roof connecting the regular set of buildings with a modular steel framework that is divided into rhomboid and triangular nodes holding up triangular glass panes. The organic skin curves in hole pillars, like a long strip of stretch fabric. The building concept is rather simple. The steel structure is like a mesh. It has a semi regular pattern of triangles, which create the funnel pillars, through the regular insertion of additional elements on the holes' diagonals, reaching a great suggestion with a rather ordinary device. Norman Foster adopted a similar pattern in his vaulted ceiling on the courtyard of the British Museum (2000). For the larger indoor public space in Europe, he designed a curved and semi simmetrical steel and glass canopy that is a fusion of engineering art and economy of form. It rests on the sidewall and on the central cylinder

with angled arcs and parallel beams. Each node of the lattice structure is unique, as the 3312 curved glass panels and each element had to be especially tailored. Each of the two Italian architects purpose then his own reading of organic design, without any expressed reference to a master, neither to the nature as Fuller did. Their relation with nature do not affects the search of structure economy by the rationalization of constructive processes but a greater attention to environment in the creation of enclosed microcosms with controlled atmosphere, as in some later Fuller’s utopian drawings of mega domes covering a whole city.

4. THE CONTEMPORARY HERITAGE. CONCLUSION Lars Spuybroek’s design approach proves to be more complex, and his writings guide the research towards auto generative design processes to the efficiency of the nature and to Frei Otto’s membranes, quoting D’Arcy Thompson work on cells balance as a result of a dynamic transformation, joining constructive rationality of light structures to organic shape of their skin. The Nox founder states Otto as his master, when he studied the chain modeling in the interaction of its elements as machine, experimenting the range of adaptability of material to forces and discovering a geometry based on material behavior. With the design of its light structures, Otto focused his attention on the generation of complex and dynamic curvatures, in a way that is similar to the topological procedures used by Spuybroek in Freshwater Pavillon (1994-97) (8). Nox’s work is a new step in the organic design and in its timely research of economy of form. The nature offers a full sample of shape efficiency in Radiolaria and single-cell organisms, and on radiolarians and cells fabric design builds its differences: Fuller assumed them as engineering model and found in polihedron symmetry the static answer to structural balance of his geodesic domes; then Frei Otto, fascinated from elastic adaptation of fluid materials, used analogical models to explain their net structures as a consequence of a dynamic process; finally Spuybroek developed their adaptability in the dynamic skin of auto generative shapes. The net patterns of the radiolarians skeleton are then the starting point of the development of organic models in light structures as self-balanced systems, while in the 60’s the study of their only apparent perfection with the availability of more powerful microscopes, lead to point on aggregative processes of their crafted pneumatic net and their adaptation to external actions. The model then turned from regular symmetry to reaction and movement, which are living actions. REFERENCES (1) Berlage H.P., Grundlagen der Architectur, Berlin, 1908. (2) Bernitsa P., edited by, Arte e Natura, italian and english texts, Gangemi, 1998. (3) Haeckel E. H., Kunstformen der Natur, 1904. (4) D'Arcy W. Thompson, On Growth and Form, 1917. (5) Fuller R. B., Tensegrity, Portfolio and Art News Annual, No. 4, 1961. (6) Fuller R. B., Synergetics – Exploration in the geometry of thinking, Macmillian Co Publishing, 1975 – 1979. (7) Heys K. M., and Miller, D. Buckminster Fulle Starting whith the universe, Whitney, Yale, 2009. (8) D. Mertins, Biocontructivism, in L. Spuybroek (2004), pages 361 – 369. (9) Museum für Gestaltung Zürich, Nature Design, From inspiration to innovation, edited by Angeli Sachs, Lars

Müller Publishers, 2007. (10) R. Piano, Giornale di bordo (Out of the blue), Firenze, 1997. (11) Spuybroeck L., NOX: Machining Architecture, 2004.