Complexity in geometry can be discovered in nature, human body, music, as well as in architecture. Though it is assumed that complex architectural structures are a result of last century’s technological evolution , complex manifolds have also been used formerly. Gaudi, was forming complex geometry structures in Sagrada Familia 100 years ago . Another example of non computer aided yet complex design, was Philips Co Pavillion designed by Iannis Xenakis and Le Corbusier, for the 1958 Brussels World's Fair.
In October 1956 Le Corbusier's sketches for the pavillion were entrusted to Iannis Xenakis, who was charged to translate them through mathematics. At the time Xenakis was working in his musical composition “Metastasis” which itself was strongly influenced by Le Corbusier's proportional scale arising out of the Fibonacci series and its association with the golden section.He transformed the graphical musical sketches of Metastasis into architectural schemes for designing the shape of Philips Pavilion .He made this through techniques, often exalted by the use of the computer, that associated the graphic construction (to compose as in writing a score) with the sonorous performance (to compose as in producing a sonorous result).The structure was a series of conjoined hyperbolic parabaloids-curved planes mathematically generated entirely from straight lines. The development of this idea into architectural form passed through a compositional process in which it is difficult to say if the mathematical structure precedes or proceeds from the architectural image.
“With the aid of electronic computers the composer becomes a sort of pilot ... sailing in the space of sound, across sonic constellations and galaxies ..." Iannis Xenakis
We can say that this is a unique compositional event which signifies that at the basis of some architectural events - perhaps those celebrating most the process of transformation of an idea from pure abstraction to factual object - were those concepts whose development is possible through the intervention of the mathematics because:
“... some relationships between music and architecture are very easy to intuit in a confused way, delicate to specify and to define, and it is not impossible to have doubts about them, because what is aesthetic is uncertain. But they seemed to me resounding. It is clear that music and architecture are both arts that don't need to imitate things; they are arts in which matter and form have relate more intimately than anywhere else; one and the other address general sensibility. Both admit repetition, an omnipotent tool; both apply to the physical effects of size and intensity, by means of which they can astonish the senses and the mind, even to annihilation. Finally, their respective nature permits an abundance of combinations and regular developments that connect or compare them with geometry and analysis.”
Xenakis's final statement at the end of his long and detailed discussion of the Philips Pavilion is:
“For the time being only cement lies at the origin of the new architecture. It prepares the bed in which the plastic materials of tomorrow will form a river rich in forms and volumes, figures that are found not only in the biological entities but above all in the most abstract mathematics.”
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