Multimand

The Multimand colouring scheme is quite interesting, colourful and extra psychedelic. I decided to make use of more of the available information to colour the graph, so i picked up the angle and velocity with which the point leaves the circle of confinement, i.e. the angle and length of the vector described by the last two values of z.

The three values - number of iterations, speed and angle - together make up the colour of the point, mapped to hue, saturation and brightness, respectively. This way, even colouring the set proper (normally just plain black), becomes viable, using the last two values of z as with any other point.

All the Multimand images I have produced so far has been plagued with a simple problem: the number of iterations of the Mandelbrot formula, theoretically mapped to the saturation value, has been effectively ignored in most instances, due to faulty scaling of the value.

The Auto-colouring Multimand is a version that automatically normalizes the three colouring parameters properly. Unfortunately, as you can see, these images get pretty boring after a while, since they fail to reproduce the pixels closer to the mandelbrot set as anything other than noise. It is still a very good way to bring out details in Julia graphs, though!