Fractals in architecture: good for the soul?


What comes into your mind when you hear the word ‘fractals’? Maths and geometry lessons? Swirly spirals in cosmic colour-schemes on student bedsit walls? Self-similar shapes in nature, like snowflakes, ferns and broccoli? The drip-paintings of Jackson Pollock?

Wikipedia says a fractal is “a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole”.

Fractal architecture is generated by the application of fractal geometric principles to the design of facades and building forms. Here are some examples of fractal architectural facades.

Yannick Joye, from Belgium’s Ghent University, argues that this type of geometry has been used in architecture for two main reasons:

1. Fractal rhythms, created by midpoint displacement, are used as a creative tool to generate a variety of architectural components, such as planning grids, strip windows, noise abatements etc. Examples can be found throughout architectural history, from Doric entablatures to modern facades.

2. The typical measurement techniques of fractal geometry are used to analyse the structure of buildings. The box-counting dimension, for example, is a measure for the recursivity of detail on ever smaller scales. An extract from Joye’s Fractal Architecture Could Be Good for You:

Carl Bovill [1996] has applied this method to different building styles. He found that Wright’s organic architecture shows a ‘cascade of detail’ on different scales, while in Le Corbusier’s modernist architecture, the box counting dimension quickly drops to 1 for smaller scales. This finding is consistent with the fact that ‘Wright’s organic architecture called for materials to be used in a way that captured nature’s complexity and order … [while] Le Corbusier’s purism called for materials to be used in a more industrial way, always looking for efficiency and purity of use’.

In the following illustrations, forms like arches and domes reoccur on different hierarchical scales throughout a Hindu temple, the Stadhuis (Town Hall) in Bruges, and the Notre Dame de Paris.

Stadhuis, Bruges

Notre Dame de Paris

However, as satisfying as fractal geometry may be to mathematicians, Yannick Joye is more interested in a less visible side-effect of fractal architecture. From an aesthetic point of view, Joye (whose specialist field is philosophy) points to research showing that human beings are innately attracted to fractals, that fractal shapes and images have a calming effect on us, and that this affinity may be related to our long-ago habitat – the trees:

… as a result of evolution, the brain has a preference for fractal structures, and feels relaxed when surrounded by these. This means that one of the reasons why we like the fractals in Gothic and Hindu architecture is that they remind us of our ancient, natural habitats. Because our brains have not fundamentally changed since prehistory, these biofilic responses are still at work.

A classic example of fractals in nature: the fern (

Do you see fractal architecture as calming and harmonious, or do you have more of a Euclidean frame of mind? I would love to see examples of the buildings that appeal to you the most.


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