The way I look at it: The pictures that we create with all of our various programs, are merely ways to visualize what is in fact a huge collection of numbers, generated by the equations. The various coloring algorithms merely let us 'see' different relationships between groupings of those numbers. Thus, when using your basic Mandelbrot set, you can have an infinite numbers of pictures resulting, dependant on whether you use a 'distance' coloring algorithm or a 'real numbers' coloring, etc.
The math itself is orderly and predictable. (It must be in order to generate any kind of mathematical solution, and thus make a picture.) The results are infinite. The final level of possible outcomes is so immensely huge, it seems chaotic to our limited grasp.
mytwocentsworth,fromanon-mathematician

RosemaryR
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"This...this is magnificent!"
"Oh, yeah. Ooooo. Aaaaah. That's how it starts.
Then, later, there's ...running. And....screaming."