RE: No matter where you are... there be STRANGE ATTRACTORS.... those lovely gems of chaos...
My first Mandelbrot set was generated by a program I typed off from a magazine. On a Commodore 64. It ran the whole day. I did not know what I was looking at, but it was beautiful and captivating in all its strange attractiveness. Pun not intended at all.
Then came Fractint...
Two decades later, and Mandelbulber generates complex 3D representations within seconds.
I showed the stuff to a friend from school, who is deeply religious and orthodox. "It is only math?" he asked, and I confirmed it: only math, as much as a parabola is only math. "No human did anything to make this?" I confirmed again: if you accept the circle as a perfect idea of which a drawing with a compass is an imperfect, approximate representation, then no human ever did anything to make this fractal except to make it visible, by drawing it with a very complex compass.
He sat in awe, looked at the picture and said "God is awesome".
Hehehe.... I might have typed some of the same code into a Commodore 64. I do know that was the first place I ever made a mandelbrot. Since it was interpreted basic it definitely was slow. You could watch each pixel slowly appear.
I love this stuff and haven't had the time to full dive into it for awhile. I will admit on this subject these days I kind of live in a bubble. I do my own experiments without seeing if someone has already done them. About the only fractal like things I've used from outside of mandelbrot and myself for awhile are perlin and simplex noise functions.
I'll look into those again!
I started, but gave up temporarily on it, writing/porting an L-System engine for POV-Ray and came to appreciate Hilbert Curves and such things... :)