Recently we’ve looked at a number of art forms which create patterns in different ways - paper art, drawing machines, kinetic wind sculptures, illusionary sculptures and the digitial display "Quantum memories." (All links are provided below^).

But what is a pattern, actually?

By definition, a pattern is something that is repeated, and is usually aesthetically pleasing. But there are different sorts of patterns, many occuring naturally in the world around us .......

.....and others created by humans using a series of mathematical equations which can be incredibly complex.

A particular type of these, known as Fractals are, in simple terms, never ending patterns where each smaller element making up the pattern is itself the same pattern as the whole! You’ll see what I mean from the following example:

Shape 1a

CLICK HERE TO SEE A MOVING GIF IMAGE fractalfoundation.wolfesongs.com

Fractals also occur in nature and include things like clouds, ice crystals, mountains, river networks, lightning strikes, flower petals, and even our blood vessel system!

Amazing lightning patterns, courtesy of Unsplash

It may astound you to know that these patterns are actually the visual representation of certain mathematical equations. It is amazing to realise that Mother Nature has known and used these equations for hundreds of thousands of years, and it has been up to humans to discover them, and develop further uses for them!

Fractals are now used in science, maths, finance, geography, art and even music! They inform our understanding of how things work, and lead to further inventions and discoveries.

A very important phenomenon of fractals is that they manifest self-similarity at all levels. Benoit Mandelbrot, one of the fathers of fractal geometry (and the man who coined the term fractal), loosely defined fractals as "shapes that are equally complex in their details as in their overall form. That is, if a piece of a fractal is suitably magnified to become of the same size as the whole, it should look like the whole, either exactly, or perhaps only slightly deformed." 1