Fractals and Mathematical Art

Fractals & mathematical art bring mathematics alive in a visually appealing way! Well-known examples are the Mandelbrot Set, and Harmonographs (popularised in science museums as devices drawing intricate curves on paper). Here’s a list of resources for you to discover more about these fascinating pictures - and how you can make your own!

Menger Sponge

Frost Patterns

A Julia Set

Nebulabrot (Buddhabrot)

Spectral Harmonograph

Escher Circle Limit III by M.C.Escher

Starship Mandelbrot


Elliptic Alien Egg

Benoit B Mandelbrot

Why is geometry often described as “cold” and “dry?” One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline, or a tree. 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.

― Benoît B. Mandelbrot

How Amazing is That?

Both the Mandelbrot & the Julia sets are generated by computing z*z+c and feeding back the result as the next value of z. z & c are so-called ‘complex numbers’, which aren’t complicated at all. It simply means that they are composed of 2 parts, ‘real’ and ‘imaginary’, like so: z=x+iy, where i*i=-1. The feedback loop is stopped either when z exceeds some value, or the loop has repeated more than some number of times. Which one happens determines if the point being tested is inside or outside the set. If outside, the size of z may be used to pick a colour for the point. Infinite complexity from a few lines of code - how amazing is that?

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