Nature, Geometry and Architecture

Our intention and philosophy is to recreate the bridge that has been lost between human and nature. The architecture then becomes a way to harmonise with the surroundings – in a living poetry

By Henry Cardona Meza

Posted on September 9th, 1999 | in Architecture
Nature, Geometry and Architecture


As an interdisciplinary research field, “Bionics” is used to express the symbiosis between nature and technology. This is the case of architecture, where the bionics method constitutes a way of exploring living systems to understand the principles of natural forms and materials for use in buildings.

Organic Architecture was a movement in which several architects like Frank Lloyd Wright and Alvar Aalto proclaimed the importance of research and analysis of natural organic life. This could result in a subsequent connection between mankind and his environment through architecture.

On the other hand, geometry mediates between nature and architecture as a methodological process. This is true, even for the effort of architects to establish ideal proportions. That was a way, in which ancient architects discovered the axiom of the ‘Golden Section’. Now we can certify a mathematical sequence of that axiom in living forms. This could explain in part, the secret of the living forms’ harmony. In particular, we should find in that way, the connection between us and the universe as a whole.


The modelling process in bio-architecture includes the systematic investigation of natural forms and analysis of their geometrical basics. In this process we usually discover an incredible precision, with which nature makes the calculations of an ideal geometry, though sometimes it is hidden from us and difficult to distinguish. But through conscious study, great sense and open soul, architect can find in such research a square of inspiration.

In this report, I would like to mention some facts which explain the importance of architecture in our lives, its influence in our sensory system and subsequent in our activities. But most important, how the degree of this influence can be determined by the real connection between architecture and nature.


What is Bionics?

In 1995 the American scientist Jackie Steele invented the word ‘Bionics’ to express a “symbiosis between nature and technology”. This is the original interpretation of Bionics, which derives from the terms ‘bio’ and ‘techniques’. But more than so, Jackie Steele believed in the principle of “learning from nature”. (1)

This principle is commonly used by different specialised sciences like mathematics, engineering and architecture. It basically constitutes a way of exploring living systems with an analytical criterion to find the better solutions for our human needs. We can also draw attention to the fact, that Bionics “is not a scientific discipline, but a certain method ”(2), in which we should implement our fantasy with an understanding of why and how things work in nature.

Bio-form, Geometrical model of construction

Bionics – an overview

View a PowerPoint presentation


1) Dr. Reinhard Witt – Bionics: Nature’s patents, 1991, page 7-§1
2) Dr. Reinhard Witt – Bionics: Nature’s patents, 1991, page 7-§4

Technology of the future with lessons from nature

During millions of years of continual evolution, nature has perfected solutions to many of the questions posed by contemporary engineers’ and architects’. But perhaps now, the most intriguing question is how can the integration of bionic findings be transformed into practice? The easiest way may be thought to be the direct imitation of nature, but this is often difficult if not impossible. Although researches have found that it is more advantageous to understand the principles of why things work in nature than slavishly copying natural models.

Early in the Renaissance period, Leonardo da Vinci drew sketches of flying vehicles based on the observation of natural principles (fig 1). He was probably one of the earliest bionicists who set the pedestal for the further development of aircraft. Other examples of bio-experimentation can be found in different fields of technology across the history. But in the area of our interest, architects like Antonio Gaudí, whose architecture was perhaps a copy of creation (fig 2), P. L. Nervi, F. Otto, E. Saarinen, among others have a long row of brilliant bio-architectural examples.

Models for Architecture

Throughout the ages, designers and architects have searched for means to assist them in the process of creation of new harmonious forms. In this way composition rules like classicism were established for architectural objects of rectangular kind. But for those objects, which remind us of organic forms, a common criterion of their characteristics has still not been adopted.

Models for Architecture 1
Models for Architecture 2

Natural spatial systems in general, have a curvaceous form. This fact makes possible the practice of such spatial composition in bio-architecture. We should evaluate the aesthetic structure and composition of those architectural objects through the method of analogy. That evaluation takes place in the conscious, because of the influence those forms can cause on the human sensory organs. That is to say reaction or acceptance. The structure of natural forms, their colour and surface texture are subordinated to the whole. In the whole of content and formation of living systems, the secret of their beauty obviously exists. Similarly, the architect’s principal responsibility is to create a meaningful form through several means by which it gives expressive qualities like scale, light, texture and colour.

Models for Architecture 3
Models for Architecture 4

The study of natural forms, in which geometry serves as a methodological process for use in architecture, is not the final intention of the bionics method. The enormous possibilities that we usually discover in natural materials and their properties led us to persist in the experimentation to develop new promissory constructive materials for use in future buildings that our fantasies can create. To inspire our imagination, we can simply try to understand the biological principle of a cable safety system along the lines of spiders’ threads. It still needs to be invented for suspension bridges.


Historical overview

Frank Lloyd Wright
Post-modern and contemporary architecture

Hugh Pearman tell us in his survey of contemporary architecture (3) that the critic Thomas Creighton, “impressed by then-new mathematics theory of universal confusion, coined the phrase ‘chaoticism’ in 1961 to describe the pluralistic activity” in architecture of this century. In contrast, the German architect Ludwig Mies Van der Rohe repeatedly remarked that “one cannot invent a new kind of architecture every Monday morning”(4). However, to confirm the position of Thomas Creighton; we have seen enormous variation of styles and movements in architecture such as New Vernacular, New Regionalism, New Classicism, High-Tech, Post-modernism, Organic Architecture, Echo-architecture, Cosmological architecture, Ultra-minimalism and so on.

We should look at this pluralism, ’chaos’ in Creighton’s expression, not as a negative architectural force, but as a logical order of human nature, which is agree with the phenomena in nature itself. A highly complex structure like the basic patterns of flora and fauna results in chaotic lines. But there is in reality a strictly ordered geometrical world. And who could fail to admire the beauty of all the variations in nature?

In the background of the modern movement, we should distinguish the prominent figures of two architects. Here we refer to Frank Lloyd Wright and Alvar Aalto, whose achievements have become excellent examples of a natural architecture.

Frank Lloyd Wright 1
Frank Lloyd Wright 2

Wright strived to create a new architecture, which he defined as ‘Organic’. It was characterised by three main architectural concepts: being “true to Time, Place and Man”(5). He also preached the beauty of native materials and insisted that buildings grow naturally from their surroundings. At about the same time that he was ignored by all, except a select following. He produced several masterpieces that exemplified the principles mentioned above. Two of them I want to allude to here: the Fallingwater house (1936), and the sculptural Solomon R. Guggenheim Museum at New York City (1956-59).

Another architect with a profound appreciation of nature was Hugo Alvar Henrik Aalto.  In his expression of the organic relationship between man, nature and buildings, he proclaimed for an ‘International Style’, not as a stylistic formula, but a way of thinking and working to be adapted to specific cultures and landscapes. He said (6) :

The very essence of architecture consist of a variety and development reminiscent of natural organic life. This is the only true style in architecture

Today we hear about similar concepts, Ecoanthropotecture, as an investigation of relationships between architecture, ecology and anthroposophy (eco – “home” : anthropo – “man, of humanity” : tecture – “of building”). This is a premise which lays claim for a conservation of our common eco-system. In contrast with the environmental problems that we have noticed on the entire planet. I relate to this movement here, because of the interesting and logical alternative.

3) Hugh Pearman (1998), page 8-§3
4) Hugh Pearman (1998), page 9-§4
5) Bruce Brooks Pfeiffer (1997), page 7 and 63
6) Richard Weston (1997), page 121


Architecture as a link between mankind and his environment
Influence of architecture in the human activities
Understanding of Social and Human needs

There were several theoretical and philosophical positions commented on above. For instance: Bionic method, Organic Architecture and Ecoanthropotecture. All have a common device, nature. But now I want to specify about the significance in the connection between nature and us; that is to say, between mankind and his environment. That connection is none other than a concrete link between the universe and us.  This is the case with architecture when it becomes an authentic artistic expression, as an integration of the whole, and not a ‘mere building’. This term was coined by Nykolas Pevsner in the opening paragraph of his Outline of European Architecture, 1942: “a bicycle shed is a building; Lincoln Cathedral is a piece of architecture…the term architecture applies only to buildings designed with a view to aesthetic appeal.” (7)

Regarding this appeal, architectural form like sound, light and colour; has the ability to create particular reactions in our sensory organs. The reaction appears later in our conscious with a greater or lesser degree of intensity; depending on how we are prepared to perceive different stimuli. So we should realise that specific perceptions of different architectural solutions can induce specific psychological aptitudes, for example, comfort or discomfort. In the same manner that “the human reaction to spatial relationships can distinguish between harmony and cacophony”(8). Proceeding from this basic conviction, we can postulate that harmony is an experience of integration (the sense of unity); and that architecture becomes a vehicle of that integration when it is harmonious, that is to say, in symbiosis with nature.

Even though this postulation can be truth with respect to the visual effect, for instance architectural form, it becomes a fact, when there is an interactive connection with the functions and techniques of buildings.

Finally we can state that architecture becomes in accordance with the society requirements, when it not only communicates the aesthetical aspirations of societies but also fulfils their practical needs.

7) Encyclopedia Britannica Online, The art of building –
8) Encyclopedia Britannica Online, Composition –


Proportional geometry

The golden section
Geometry and Music

Already architects from ancient Greece developed complex geometrical compositions in their architectural masterpieces (see fig 3). This was an effort to establish ideal proportions that led them to discover the axiom of the ‘Golden Section’ also called the ‘Divine Proportion’ (9). According to this axiom, a line should be divided into two unequal parts, of which the first is to the second as the second is to the whole. To adapt this axiom to our figure shown below, we can say that the entire segment L is to the larger part M as this part is to the smaller m (see figure below). This “asymmetrical division creates the dynamics necessary for progression and extension from the Unity”(10).

golden ratio

The previous observation is not the only one that can be deduced from this amazing geometry. There are grand philosophical, natural and aesthetic considerations, which have surrounded the golden proportion along the history. But the fact is that its presence can be found in Nature. Even though it is designated by the 21st letter of the Greek alphabet, phi Φ, it was known by cultures much older than the Greek. Although, the Greeks were the civilisation in which, we find the practice of the Divine proportion more widely used.  They developed out a compositional theory around the ‘Golden Rectangle’, which was considered by them to be the most pleasantly proportioned of all rectangles (see fig 4). They believed that, for the ideal beauty of any figure (including the human form), the various parts should have the proportions of the golden ratio. Curiously, there are wide existence of postulates with the argument that the golden proportion represents indisputable evidence of the possibility of ”conscious evolution” as well as of ”an evolution of consciousness”(11). We could say, that the evolution itself of any organic forms is closely connected with the geometrical proportion of the Golden Section.

Proportional Geometry 1
Proportional Geometry 2

In 1202 the mathematician Leonardo of Pisa, also called Fibonacci, worked out a mathematical explanation of the axiom that is known to modern mathematicians as the Fibonacci sequence. The Fibonacci numbers are defined by the function: f(n)=f(n-1)+f(n-2); for n/3. The few first terms resulting from the function are 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377. These numbers have many interesting properties, which in the 19th century aroused the interest of the French mathematician Edouard Lucas. Then scientists began to discover such sequences in nature; for example, in the spirals of sunflower heads, in the regular descent (genealogy) of the male bee, and in animal horns amongst others.

Based on the same axiom, Leonardo da Vinci developed a figure of the ideal man, and in the 20th Century, the French architect Le Corbusier developed a theory of proportion called ‘Modulor’.

There is another interesting fact I want to mention here, which demonstrates how architecture becomes music; and geometry is the channel that makes it possible. It was explained by Hans Jenny in his work Cymatics I and II (1974) and states thatwe can begin to see the relationship of form and sound in the physical world”(12). His experiments have shown that sound is an instrument through which temporal frequency patterns can become formal spatial and geometric patterns. These patterns can result then in a mathematical logarithm which show the Golden Proportion as the archetype for this form of growth i.e. effect of addition and multiplication (fig 5).

Cymatics water sound
Cymatics water sound – source:

9) Kepler’s Discovery –
10) Robert Lawlor (1982) – Sacred Geometry, page 47
11) Robert Lawlor (1982) – Sacred Geometry, page 45
12) Hans Jenny (1974) – Cymatics I and II, a study of wave phenomena and vibration.


The idea of Cosmic Man
The Modulator, Le Corbusier
Anthropometry 1
Anthropometry 2

The idea of Cosmic Man is reflected in a mystic doctrine called anthropocosmic. The first principle of this doctrine postulates that ‘Man is not a mere constituent part of this universe, but rather he is both the final summarising product of evolution and the original seed potential out of which the universe germinated’. A pure metaphysical position telling us that ‘God created the universe from a desire to see himself and to adore himself’ (13). Let us for a moment leave the debate about God to the theologians and instead, assume that what is being described is the relationship between the whole and all its parts, between the macro and the micro. I believe, this relationship doesn’t need any proof to be admitted. On the other side, as a particular part of that whole, Man is in himself an individual, surely with an unique expression of live.

Through an identification with the essential universal proportions expressed through the ideal human form (fig 6), each individual man may contemplate the link between his own physiology and universal cosmology, thereby envisaging a relationship with his own universal nature. This array of universal proportions within the body of Ideal Man becomes the basis in Le Corbusier’s thoughts that led to the elaboration of the first bases of the ‘Modulor’ concept as we commented above. This concept is a scale of harmonic measures, based in the golden section that set architectural elements in proportion to human stature.

13) Robert Lawlor (1982) – Sacred Geometry, page 90

Geometry of Universal forms

Model of natural cupolas
Construction of steel cables and steel plates, Kenzo Tange
Elasticity an resistance of vertical structures
Complexly forms made by single components

There is a good reason why architects in the past chose domes and arched vaults as their designed forms when they wanted to enclose large interior spaces. In analogy with a natural shell, there is no other shape in building with which it is possible to implement roofs with virtually any span, and yet use the minimum amount of material.

The spiders’ web as another natural model, which constitutes a remarkable example of elasticity and stability. The architect and engineer Frei Otto experimenting with those principles has constructed several architectural complexes, that enclose in their essence rather a visual effect than an authentic function which the spiders’ web has, for instance, catching. But the possibility of continual experimentation is still in life.

Basically, metal frames are nothing more than construction engineering copied from nature. Masterly solutions to the static problems have been found in this way, for example Eiffel Tower (France), Paxton’s Crystal Palace (London), the television tower Stankino (Moscow), where a tall tubular construction has a natural equivalent namely corn stalk, among others.


From a personal point of view…

When we pose the simple question about the meaning of life, we usually come to different opinions depending on our personal experiences. But in fact, most peoples’ goal can be the search for their happiness and good fortune. To accomplish this effort, architecture should innovate our surroundings with natural and harmonic solutions. Solutions that could integrate us with the universe around us. On the other hand, nature has the key for that integration, in which humanity doesn’t need to look so far from itself.


  • Bionics : nature’s patents / editors-in-chief: Dr. Reinhard Witt, Claus-Peter Lieckfeld, 1991
  • Brooks, Bruce Pfeiffer and Larkin, David, Frank Lloyd Wrigth, Master Builder,1997
  • Lawlor, Robert – Sacred Geometry. Philosophy and practice. For R. A. Schwaller de Lubicz and Lucie Lammy, 1997
  • Mijailenko, B.E. and Kashenko A.B. Bionics and Architecture, Kiev 1981
  • Pearman, Hugh. Contemporary world architecture, London 1998
  • Weston, Richard, Alvar Aalto, London 1997
  • Bionics and Evolutiontechnique,
  • The Frank Lloyd Wright Foundation Home Page:
  • archINFORM – International Architectural Database:
  • Design Matrix Bionics References:
  • Cymatica – an architectural investigation exploring the synthesis of spatial proportion and form generated from sound:
Leave a Comment