The last week or so, as well as working on the mixes for my first album, I decided to have a look into fractals as it seemed like a logical next step from the graphics animations I have been working on so far. I found that Wikipedia has a lot of good resources, but probably has too much detail for a beginner, if you follow all the rabbit holes it leads you down like I did. A far better introduction was a Youtube video, which brought together pretty much everything I’d read to date and then some. (Sadly it’s been taken down since I wrote this post so I can no longer share it with you).
At least some of the more visually appealing fractal patterns are constructed using maths that involves the square root of minus one, eg Mandelbrot and Julia sets. Those sets also looked as though they were not going to be easy to animate, as it looks like the whole image is calculated pixel by pixel, with the colour of each pixel set by how long it took to reach a threshold value.
There are some (more basic) fractals that were more easy to understand, however, such as the Cantor set and the Sierpinski carpet, which are made by an iterative process. The Cantor set is a set of lines with the middle section taken out. Then you rinse and repeat, taking the middle section of the new lines away for the next iteration. The Sierpinski curve does something fairly similar, but with rectangles. I could see a way through the fog for programming visuals for these types of fractals in Processing, and have incorporated some of these into a new set of visuals for displaying during my next live gig.