Fractals

Fractals are geometric shapes that repeat themselves as the scale changes. The term ‘fractal’ was coined by Benoit Mandelbrot in 1975 for mathematical sets of numbers that stay ubiquitous despite the scale at which they are viewed. These are never-ending patterns that are self-similar. The property of self-similarity refers to the property where the object retains its original proportions even after it undergoes a transformation.

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Example of a Fractal_©unsplash.com

Several architectural styles have their principles based on the inspiration of nature. Fractals provide a medium for the expression of irregular, organic curves, and natural shapes. They help reduce the complex patterns of nature to something comprehensible. Fractals are naturally present all around us, from the growth of pineapples and pinecones to the formation of ice crystals and tree branches. Hence, it only makes sense that architects looking at nature for inspiration applied fractals in their structures as well.

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Fractal in Nature_©unsplash.com

Fractal geometry in architecture can be found in two ways- unintentional or intentional. Unintentional fractal geometry is usually found in cases of aesthetics, where the fractals create a repeating pattern that is visually appealing. Intentional fractal geometry is created purposefully with a specific idea in mind. 

Fractal Geometry in Hindu Architecture

Fractal geometry in Hindu Temples is prominent in the design of the shikhara, which is a significantly large characteristic tower, symbolic of a mountain peak. The fractal arrangements owe their existence to the desire of the people to have the tower resemble the contour of a mountain with its varied heights.

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Fractal Geometry seen in Kandariya Mahadeva Temple, Khajuraho_©www.kevinstandagephotography.wordpress.com
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Fractal Geometry seen in Kandariya Mahadeva Temple, Khajuraho_©www.kevinstandagephotography.wordpress.com

The fractal nature of the Hindu temple is also closely related to Hindu philosophy about the universe. In Hindu philosophy, the universe is seen as a whole, where each part of the whole is whole itself. This is also reflected in the plans, where the plain sides are replaced by interior and exterior projections.

Fractal Geometry in Buddhist Architecture

Borobudur, a Buddhist stupa in Indonesia, Java, exhibits fractal behaviour. The entire structure is made in the form of a lotus, a stepped pyramid of six rectangular stories, three circular terraces and a central stupa forming the summit. When the plan of the structure is seen, it shows the design of a mandala, the largest in the world.

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Borobudur, Indonesia_©unsplash.com

Fractal Geometry in Gothic Architecture

Self-similarity is visible in the elegant facades of the gothic structures. There is a repeat of basic, regular elements throughout the elevation in varied heights and widths. There is a recurrence of arched forms and motifs throughout the structure in different hierarchical scales. Here, the shape of the main entrance is repeated in smaller dimensions in the arched windows on either side, which is further repeated in the small openings and niches. Gothic architecture is also very detail and pattern-oriented which adds to the fractal character of its structures.

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Gothic Building Facades in Belgium_©unsplash.com.jpg

Geometry was used in gothic architecture as a means of conversing with the universe through mathematics. The fractal nature of the structures creates an unlimited scale, very detailed and appealing to see. The walls, ceilings, pavements, and facades all have minute patterns that repeat and are self-similar. The subtlety of these designs registers in the mind very minutely and creates beauty.

Saint Peter’s Dome in Venice also has iterative domes at different scales. The structure has a central, cross-shaped aisle with symmetric clusters in between its arms. These arms further consist of smaller crosses. 

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Plan of St. Peter’s Basilica, Rome_©etc.usf.edu.jpg

Fractal Geometry in African Communities

There is a rich variety of fractal examples in architecture that can be seen in African communities. Self-similar structures are arranged according to the religious and social status and power of an individual in a society. Their entire settlement has the same ring-like shape, with smaller rings popping out of the circumference of the main ring.

Each extended family has a ring-shaped fence with a gate. There are storage buildings and dwelling structures arranged around the ring. The dwellings get larger as they approach the peak of the ring and the largest house is that of the village chief or head member of the clan.

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Fractal structures of Southern Zambia_©ograndejardim.com

Fractal Geometry in Modern Architecture

Frank Lloyd Wright’s structure, Palmer House, shows fractal nature in its floor plan. However, it can be said that the fractal character is more influential when viewed in three-dimensional form rather than in the plan, where it is barely visible. Another Wright building, the Marin Civic Centre in San Francisco, also shows the fractal character in its front elevation.

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Plan of Palmer House_©yelp.com.jpg
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Elevation of Marin Civic Center_©www.franklloydwright.org

Another twentieth-century Russian artist, Malevich, created impressive three-dimensional fractal structures. His models, collectively called Arkhitektonics, are marvellous examples of creating buildings with similar elements on numerous scales. 

The fractal nature of a shopping mall in Addis Ababa, Ethiopia, by Xavier Vilalta, is also noteworthy. Its design is based on fractal geometry and has been inspired by the bold patterns on the dress of Ethiopian women. The architect has also used fractal geometry in his other structures, such as the Lideta Mercato in Ethiopia and the Melaku Centre Campus in Barcelona.

Lideta Mercato in Ethiopia_©www.blog.ted.com

Conclusion

Buildings with fractal components have a strong aesthetic pull, attracting the viewer towards them and presenting a very pleasing appearance. This aesthetic appeal can be chalked to the fact that humans display positive emotions towards nature. Since fractals replicate complex natural shapes, they inspire a sense of ‘biophilia’ among the viewers. 

References:
  1. Shea Gunther – Tree Hugger (2022). 9 Amazing Fractals Found in Nature. [online]. Available at: https://www.treehugger.com/amazing-fractals-found-in-nature-4868776 [Accessed date: 03/06/2022].
  2. Kate Torgovnick May – TED Blog  (2013). Architecture infused with fractals: how TED speaker Ron Eglash inspired architect Xavier Vilalta. [online]. Available at: https://blog.ted.com/architecture-infused-with-fractals-ron-eglash-and-xavier-vilalta/ [Accessed date: 03/06/2022].
  3. Sala, N. (2006). Fractal geometry and architecture: some interesting connections . WIT Transactions on the Built Environment, Vol 86. Available from: https://www.witpress.com/Secure/elibrary/papers/ARC06/ARC06017FU1.pdf. [Accessed: 02/06/2022].
  4. Joye, Y. (2007). Fractal Architecture Could Be Good for You . Nexus Network Journal, Volume 9 (2). Available from: https://link.springer.com/content/pdf/10.1007/s00004-007-0045-y.pdf. [Accessed: 02/06/2022].
  5. Bovill, C. (1996). Fractal Geometry in Architecture and Design . Nexus Network Journal, Volume I. Available from: https://link.springer.com/content/pdf/10.1007/s00004-998-0014-0.pdf. [Accessed: 03/06/2022].
  6. TED. (2007). Ron Eglash: The Fractals at the Heart of African Designs. [Youtube Video]. Available at: https://www.youtube.com/watch?v=7n36qV4Lk94. [Accessed: 02/06/2022].
Author

Kanak Holani is a first year architecture student who can usually be found reading novels and trying her hand at various crafts. She is passionate about history, culture and climate and how it all ties in with architecture.

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