The Inexplicable Attraction of Fractals
Fractals are one of the world’s most amazing mathematical concepts. We see their manifestations both in the environment around us, and even in ourselves. Put in a dry scientific language, a “fractal” is a set with the property of self-similarity, meaning the parts of the object have the same form as the object itself. It is not so easy to imagine such an abstraction. Indeed, the essence of this self-similarity is best conveyed by the following render:
It is a 3D version of the “Sierpinski triangle”, a 2D fractal belonging to the class of geometric fractals. Much more complicated is the “classic” look of the Mandelbrot set, a member of the algebraic fractals. This fractal is named after mathematician Benoit Mandelbrot, who in 1975 first proposed the term “fractal”. It can be built using the simple equation:
The most fascinating part of fractals is that they can be increased almost indefinitely, with strict adherence of their transformation into themselves. Here’s an example with the same Mandelbrot set:
Although the property of self-similarity has been known to mathematicians since the nineteenth century, for many years such sets were not allocated in a separate class. In nature, fractals are everywhere around us: branching veins in leaves, the structure of trees, the blood circulatory system of the lungs, frost structures on glass — all of these are examples of fractal-like structures.
It is curious to note that when Benoit Mandelbrot published his study results in the late 1970s, many people thought fractals were a useless amusement, a waste of time without the possibility of practical application. However, not everyone shared his opinion. Loren Carpenter, one of the future founders of the now global Pixar studio, was inspired by Mandelbrot’s calculations, and used his “fractal” formulas to generate a mountain landscape on a computer — a real breakthrough for the time. In 1980, Carpenter also rendered the short Vol Libre video using fractals, after which the author was invited to develop special effects at Lucasfilm studio.
Fractals revolutionized computer graphics, when with the growth of computing power, it became possible to generate realistic landscapes, water surfaces, vegetation and much more. Today, this can be done on any average computer, it does need to even be very powerful.
Fractal calculations are also used in the compression of digital images, providing high compression with minimal quality losses, and also for the modeling of non-linear processes in physics, including the behavior of fluids, vapors, flame, mixing of various substances, and so on. Fractals are used in biology, medicine, and a number of other Sciences and applied areas.
Thanks in particular to their connections with many branches of science, we decided to use fractals ourselves. Now our site smatrz.io is designed with renderings based on Mandelbrot sets. There are many tools available on the internet to create fractals, but we especially liked this one sunandstuff.com/mandelbrot. After receiving the author’s permission, we modified the generator to suit our needs:
Then we experimented with fractals of different types and colours for a long time. Eventually we came up with the set we now use in our identity:
But since we’re truly inspired by fractals, we need to use them in full!
Therefore, soon afterwards we also came up with a logo in the form of a fractal as well. Only this time, instead of the Mandelbrot set, the leading role is played by the Sierpinski carpet. :)
