Sometimes Maths Can Be Beautiful

I’ve always been interested in the visual aspect of mathematics.  Beyond simply drawing something out on a graph, I’m talking on a much larger scale.  The idea of fractals.  

Patterns, where their detail changes according to the scale that they are measured at.

Fractals appear in a variety of places: they can be found in nature - vegetables for example the Romanesco brocolli (pictured above courtesy of Jon Sullivan) resembles a repeating spiral pattern that is totally symmetrical and repeating.  Also in nature - the typical lightning pattern or ‘Lichtenberg figure’, forking indefinitely - this can be seen in the two examples pictured above (courtesy of Bert Hickman), one where an electrical discharge is being directed through clear acrylic, and the other showing what is left over after the discharge has passed through the material.

In terms of computers, complicated mathematical formulae can create fractal images - stunning patterns akin to something that could of been drawn by a famous contemporary artist.

The following website created by Jock Cooper hosts a large array of intricate fractal patterns that have all been produced through this idea.  Some are zoomable - showing how the pattern repeats infinitely the more you zoom in on the pattern.

http://www.fractal-recursions.com

I have selected a few examples (all courtesy of Jock Cooper’s huge repository of pictures) of what I personally think are the finest examples of what can be achieved by the process of computing fractals. 

The pictures range from traditional spiky fractal patterns, to huge squared-edged mechanical looking patterns, to kaleidoscope patterns and combinations of many curvy patterns.