Fractals

I’ve just updated my blog header to use part of an old fractal wallpaper. It’s a part of the Mandelbrot set, located somewhere between the second and third bulbs.  I foolishly forgot to make a note of where, because I like that region of it and I’ve not been able to find it again since!

The formula for the set is famously simple:  the colour of a pixel at point c is determined by how many iterations it takes for z -> z² + c to escape from the origin (usually tested as |z| > 2).  This gives us beautiful monochrome images, but I’m still looking for a way to add colour information.  (The images can be colourised by mapping the greyscale levels to hues, but that’s still monochromatic IMO.)  I have a hunch that the related Julia set might be used to inform the colour for each pixel — each pixel corresponds to an entire image in the Julia set.

PS. The complete wallpaper and a couple of other images are still on my non-blog.