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Chalk drawing by roger Johnston

Mandelbrot and Fractals: Different Ways of Perceiving Space


The universe resembles itself, and mathematics can give us a glimpse of this self-similarity.

Mathematics has always placed a greater emphasis on algebra, a “purer” version of itself, one that is more rational at least. Perhaps like in philosophy, the use of a large number knotted concepts in a multi idiomatic sentence structure reflects a deeper analysis, a greater purity or an intellectual cleanse —which we know is not necessarily always the case. ‘The intellectual impostures’ that Sokal and Bricmont criticised, in an effort to prove that there are times when complex expressions and concepts only work against a text, they drain the key arguments from any sense of depth. Whether we believe they are right or not, their book actually lacks a useful argument to support their theory, and additionally it shows a complete misunderstanding and poor knowledge of the authors and theories it criticizes.

Green succulent plant

The field of mathematics was undergoing a similar situation when Benoît Mandelbrot (1924-2010) and his fractals appeared on the scene. At the time, Euclidian geometry was widely favoured, naturalising it, forcing all objects on Earth to correspond with it. One of his most famous phrases is: ‘Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line,’ (Fractal Geometry of Nature, 1982). In this sense, this Polish innovator hands us a vision, that is, well, more visual of real, existing forms than merely mathematical ones.

Fractal geometry, the root of the word comes from fractus Latin for broken, fractured, is characterised by a more abstract take on dimension, unlike conventional geometry. Ultimately, what Mandelbrot does, is create an installation, which the awareness of our perception of the world and its forms is visually shattered. He changes the way in which we see reality, establishing an unprecedented new perspective. In other words: by forcing us into abstraction, he brings us closer. His contributions become a new epistemology on vision, which also questions the value we give a certain branch or another within a single discipline

close up of intricate pattern

Since then, fractals have been a tool that has been used graphically represent huge amounts of information over time (the movement of meteorological phenomena, the medium level of an area’s crops, additionally it is of the utmost importance in terms of understanding electronic formats). The principle behind Mandelbrot’s self-similarity, which proposes a condition where, on different scales, the individual pieces retain the same overall proportions, is also a tool that enables a new perception of the universe, since it can be contained, in its entirety, within a single speck of dust.

For further reading on the Mandelbrot set, follow this link.

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