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quaterdrop

or

Mandelbrot: s/ℂ/ℍ Edition

Named thusly 'cuz it kind of looks like a water drop at the top level. Also quaternions.

This is a GPU program that draws the Mandelbrot set, using quaternions instead of complex numbers. (Quaternion fractals aren't a new idea, except to me.)

You probably want a reasonably good GPU.

Something approximately equivalent to the Julia Set available by editing main in fragment.glsl. It's somewhat more difficult to find interesting space in it; an iteration depth of 200 is recommended.

The fractal viewer bit is forked from remexre/mandelbrot-rust-gl.

Controls

left-drag: pan x,y
right-drag: pan z,w
scroll: zoom (x,y)
r: reload shader
o/p: change iteration depth limit by 1
lbracket/rbracket: change iteration depth limit by 10
space: reset zoom
period: print out draw parameters

Interesting features

Collect all n.

  • Maelstroms
  • Theaters
  • Spooky ghosts
  • Creepy masks

Here's some other picture.

In general, the fractal is less regular than Mandelbrot, more wild & surprising. Unlike Mandelbrot, there are edges where recurrence ceases. Regularly recurring features are rare, but have been found.

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