“I know this world is ruled by infinite intelligence. Everything that surrounds us- everything that exists – proves that there are infinite laws behind it. There can be no denying this fact. It is mathematical in its precision.”
-Thomas A. Edison
There is something magical bound to happen when we combine art and math. The amalgamation expands our vision of what it means to be an artist and a mathematician. Math can be creative. Art can be analytical. Both can inspire our imagination.
Chaos theory, the branch of mathematics that deals with complex systems whose behavior is highly sensitive to slight changes in conditions so that small alterations can give rise to strikingly great consequences. The development of chaos theory creates a new perspective for a better understanding of chaos and complex processes in architectural design. It is relatively easy to distinguish between geometric order and chaos in architectural compositions, but defining these concepts is certainly difficult.
In the urban structure of Barcelona, the subtle combination of the same is visible today. In the 19th Century when the walls were pulled down, a large extension of the city was realized. This new part of the city was organized in grids to achieve over 600 identical urban blocks – 110m X 110m with angled corners. Over time, all these blocks were developed in their individual way. This example leads to formulating a conclusion that chaos precedes order and order precedes chaos and there is beauty somewhere in between.
From centuries architects and structure engineers have been looking at nature as a huge source of inspiration. They have been searching for answers to their complex questions about different kinds of shapes, structures, or processes, and they have mimicked a lot of natural forms to create better and more efficient structures suitable for different architectural purposes. But to what extent have they been successful? The world of Nature is constructed according to more complex rules. The ideal forms and relationships distinguish architecture against the background of nature. The glorification of complexity and regularity exists also in the architectural design of the present time. Many well-known architects – Zaha Hadid, Daniel Libeskind, Frank O. Gehry take inspiration from chaos.
In the first two years of architecture course, the college engraves in us the habit of keenly observing nature and drawing inspiration from it into anything we create. Throughout the next 3 years, we keep putting our minds into drawing the “order” stimulated by what we see in the immediate environment. But are there tools for simulating, analyzing, and understanding chaos? As architects, we are drawn to certain limitations to jump from order to chaos. These limitations concern the classic design and the Computer-Aided Design (CAD) as well. This technique was developed dynamically in the 90s to increase the effectiveness of architects but fundamentally – hasn’t changed design methods. Parametric Modelling is an example of an alternative, more complex methods of computer-supported architecture design. But the simulation of a complex process that occurs in architectonic space using this method is not realistic. Then how do we obtain complex geometry?
The creation of architectural space is not an isolated event, but the continuous process of technological modernizations, destroying, adapting, and property changes. In the scale of the city, the accumulation of this process causes spatial diversity and complexity. This is not a consequence of conscious design planning, but free transformation. In this case, architecture starts to be chaotic. Reflecting on the way cities have been built through history, the most beautiful places have been those that have shared transformations while creating differentiation. The city of Venice continues to inspire architects despite their inability to live up to its beauty – is a perfect example of shared transformations creating wholeness out of chaos. Without order, nothing can exist and without chaos, nothing can evolve and this recursive pattern opens a window of fractals into exploring complex geometry of chaos.
Architect Robert Venturi when rejected the theory “less is more” and contracted it with his own “Less is a bore”, refused the plainer, clean, white architecture of modernism, instead; his ideas were directed to indirect architectural design, meanings, forms, and compositions which satisfy the mind. He believed that complexity makes one think of how things are put together; it takes time to be perceived and decoded. What Venturi was aiming for in architecture was actually found in the characteristics of fractal geometry as it plays an integral role between natures’ complexity and architecture.
While two buildings may have completely different sizes or roofs, or one could have a Minar and the other doesn’t, if both the buildings have windows and columns the windows and columns would be made the same way, and thus symmetric to each other. This is how every building in the city is tied together in a web of geometric relationships, and it is the density of these relationships that give cities their wholeness and beauty.
The fractal theory fully supports the Hindu philosophical concept of ‘one among all, all is one.’ This might be the root reason for the use of Fractal Geometry in the architectural design of Hindu Temple Architecture. The self-repeating and self-similar components are supposed to reflect the idea that every part of the cosmos contains all information about the whole cosmos with a high degree of self-similarity and complex detailing. Each element of these temples reveals the mystery of these gigantic structures folds by fold. From an aesthetical viewpoint, fractal geometry brings about “order in chaos” and thereby, “a beauty in complexity”.
If fractals are, by their own nature, surprising, unpredictable, and emergent, I ask you – artist to artist, designer to designer, architect to architect – do you have the courage to dive in the depths of the beautiful possibilities of chaotic geometry? I am sure, I do. Living in the 21st century, let less be a little bore for you. Let your creative mind magnify the order a little more, only to find the chaotic beauty in it.