A friend asked the other days what was up with all the fractals on my site and it reminded me that I’ve neither mentioned them in my blog or even sat down and created any for a while, so I thought I’d remedy that, especially since I now have the personal section so I don’t have to bother planet readers with this stuff.

Fractals fascinate me for a couple of reasons. The first is obvious, they are in general strikingly beautiful. Even the most basic fractals with simple colouring choices look stunning and because of how they are created can be generated at any size with no loss of detail.

The second reason is due to how they are generated. Like most developers I’m a pretty mathematical sort of guy, equations and algorithms can actually interest me (sad I know). It amazes me that such images can be created from essentially simple equations. Take the most well known fractal, the Mandelbrot set. This is generated using the following iterative equation

z_{n+1}= z_{n}^{2}+ c

That’s it. Well that and understanding how to apply the formula, using complex numbers and using a suitable colour palette. But still, such a simple looking formula generating something that looks beautiful and repeats infinitely at many zoom levels seems awesome to me.

The final reason is because I can actually generate my own images. I’m not what you’d call much of an artist. I like to think I can generally recognise what looks good, but creating something from scratch is beyond me. Fractals let me do this because really I’m not creating anything from scratch. I’m starting with some formula that is known to work well, choosing colouring methods, choosing colour palettes and tweaking parameters until I am happy with the results. Obviously that means I’m still no artist, but I like to think that many of my creations look good. All of the fractals in my media gallery were created by me, using a few different fractal generating programs.

I’m going to try to blog about my fractals when I make a new one from now on, if there is anything particularly interesting to say at least. The one attached took a long time to create. It is fairly easy to create good looking fractals at random, but trying to design one around a particular goal is much harder.

I did a course on chaos theory at uni which finally ended up with generating fractals and the importance of them. I was surprised at the simplicity in which they were generated, it was funny to see the set of ‘equations which behave nicely’ was so small compared to the chaos side of things.

Check out some interesting fractal images I created at: http://www.fractalsciencekit.com/tutorial/examples/examples.htm

I am constantly amazed at what math can produce!