Throughout my studies at University for my maths degree I did courses in all sorts of different topics – but because of the sheer number of courses that were on offer I never got round to doing the course called “Fractal Geometry”. Which is a shame.

What is a fractal? Fractals are not easy to define; even among mathematicians there can be disagreement about how to define a fractal – but a fractal is something that, loosely-speaking, displays some degree of self-similarity at all levels of magnification. In other words, you could zoom in as much as you want on a fractal and what you see will in some ways resemble the original fractal.

Although I suspect that the course at Warwick would have been more concerned with the theoretical aspects of of fractals and fractal analysis, the fractals that are actually being analysed can be very interesting and visually appealing.

Probably one of the most famous fractals is called the Mandelbrot set – it looks like this;

The Mandelbrot Set

The Mandelbrot Set

This fractal can be created using a very simple formula that someone with even a basic understanding of mathematics can understand. Not only is this fractal interesting from a theoretical perspective, I think it is also interesting from a visual perspective. From this single fractal it is possible to generate countless different fractals such as these Julia Sets

Julia Set Julia Set 2 Julia Set 3

The above images were produced using some fractal-generating software that is freely available, and surprisingly easy to use, called Fraqtive.

There is a considerable amount of theory surrounding fractals; I’m working on learning some of the theory but for the time-being it doesn’t stop me from appreciating how beautiful these things can be.

The Mandelbrot set is just one example of a fractal – there are millions of other examples, each of which has its own character. Fractals appear all over the place, probably without you even noticing them.

No doubt I’ll be coming back to fractals at some point in the future.