Chaos Theory, Fractals, and Architecture


Countless natural patterns can enhance design and architecture to be one with nature. Fibonacci and the golden ratio enable us to create a proportion that makes the space seemingly cohesive, which I presented in a previous article. Our environment has many patterns that we can draw out to design spaces and model systems. Chaos theory and fractals are some of these natural principles. Chaos theory is a fascinating subject to dwell on despite few who only understand it, but countless heard this principle. In chaos theory, we can see the order in chaos, which a pattern emerges from it. We see chaos as an entirely random series of events, but as we continue to observe chaos, we can see beautiful, some people say godly, pattern in it.

Inherent to chaos theory is the hypothesis of causality that exceedingly small changes have massive impacts like butterfly flaps its wings in our place, and it causes typhoon 100 miles away. It may vague at first, but it seems truthful in some sense if we understood in retrospect, which accurate forecasting is nearly difficult. We take climate change as an example. A small drop or increase in seawater temperature has far-reaching consequences on our weather. Or we can consider global warming by one degree Celsius higher, and our world's seas can't hold carbon dioxide due to a chemical quirk.

We can apply chaos theory in several fields, like economics, neuroscience, physics, and even architecture, to name a few. There are systems across our universe and the environment that is intrinsically chaotic and unpredictable. But it tends to become orderly. Life is an expression of self-organizing systems, which is profound given that we are unaware of the processes leading to the genesis of life in the first place. But the unlikely profundity of chaos theory extends even further for humans. Our brain fires neurons in a deterministic path, but the cascaded reaction becomes unpredictable afterward.


One aspect of chaos is the pattern that emerges from it. We called it fractals. A fractal is a pattern that never ends, with complex patterns having self-similarity at different scales. We can found fractals everywhere. Tree branches have their branches that, when we zoomed in, look strikingly similar to the larger branching patterns. The nerves in our body spread out in similarly repeated patterns. We can found too in the bronchial structures of our lungs. We can observe fractals in cities as they grow and spread out. Fractals are many ways of experiencing infinity.

Fractals don't have straight lines and smooth curves in that they are fractioned and lack a tangent at any given place, such as the Koch curve, the Minkowski curve, and the Peano curve. It is different from Euclidean geometry. Fractals theory enables us to interpret natural patterns that are not possible mathematically with classical mathematics. We can have a sense of self-similarity in fractals. It is an aspect identifiable at all scales, except for the physical limits of reality to reach infinite iterations.

Fractal architecture makes use of fractals in designing spaces and buildings. The use of fractals in design and architecture is not new. We can see heavily influenced fractal structures in Hindu temples and other sacred buildings. We can observe the self-repeating and self-similar components that align and reflect the belief that we are one with the universe. It is as if portraying these spaces and buildings as part of the grand design of the universe.


Yannick Joye emphasizes that we feel good in the space in one with nature due to its fractality, but not its natural elements. He shared that we have positive responses to fractals despite the lack of natural physical components in certain paintings and architecture. Our attraction to fractal dimensions stems from our biological need to find sustainable habitats that are one with nature. These habitats exhibit biophilic feature that explains why we love fractal geometry architecture and why it is good for us.

Fractal architecture is not just biophilic but also biomimetic. Biophilic draws out our innate attraction to nature while biomimetics design with nature in mind. The fractal architecture combines both concepts, which is why we drew too much to it. We can design canopies that exhibit the pattern of tree branches and use a natural element to them. We can also incorporate the lotus effect, a term describing self-cleaning drawn from leaves. We can achieve the lotus effect by studying the fractal structural patterns of leaves and insect wings on why it is hard for dirt particles to stick and integrate them into our design of spaces and systems.

We saw fractal geometry embedded in traditional architectural composition in temples and sacred places. Maybe our ancestors used it as a creative tool, but Joye subsequently reveals that there is a much deeper rationale why we started mixing fractal forms in our architecture. Architects and designers became fascinated with fractals due to our inherent desire to capture nature's complexity and order. It seems clear that biophilic architecture resonates with fractals due to our quest for sustainability and conduciveness.


There are arguments that our use of fractal is more aesthetic than functional. I think it isn't. Architectures aim to achieve functionality in a space rather than too aesthetically, and with that in mind, architects tend to find a natural way to make a space cohesive. I think fractal and natural patterns offer both functionality and aesthetics. Furthermore, the distinction between utility and aesthetic worth may get muddled, as who is to argue that artistic expression is not a necessary architectural function? The aesthetic features of a building boost the feel of the space. In some sense, functionality and aesthetics intertwine.

Hindu temple is an example of fractal architecture, which the temples adhere to Hindu's belief of fractal cosmology. Hindu exploited different ways to merge fractals with its architectural designs, whether horizontal, vertical, or radial integration of repeating patterns. Gothic Architecture also resembles a lot of fractal architecture, such as Notre Dame Cathedral in Paris and City Hall in Bruges. These architectural masterpieces have fractals on different scales.

Although few people comprehend it, chaos theory is a fascinating subject to study. Again, we can find order in chaos, and a pattern emerges from it. We can observe fractals in different places, including tree branches and bronchial structures in the lungs. Our fascination with fractal dimensions stems from our biological need to find a way to become one with nature, in some sense. Biophilic stimulates our natural attraction to nature, whereas biomimetics designs by imitating nature. Both concepts are in fractal architecture. It's impossible to quit thinking about chaos theory after reading about it. When asked where we see ourselves in five years, point to chaos theory and say we may be anywhere, from joining a traveling circus as a trapeze artist to going to distant stars or building the tallest structure man never yet to know. After all, it is scientifically safe to say.


  1. Yannick Joy, Fractal Architecture Could Be Good for You, Springer

  2. Robin George Andrews, Nietzsche's Butterfly: An Introduction to Chaos Theory, Nature

  3. Majalinse, Fractal geometry in nature and architecture, Spatial Experiments

Photo Credit:

  1. Mandelbrot Set by Wolfgang Beyer

  2. The City Hall of Burges by Michael D Beckwith

  3. India Temples by Volker Glätsch

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