N-dimensional complex numbers

Lont time ago when I was in high school I had a fascination for quaternions and wrote a mandelbrot implementation for them in a weird c like language on the Amiga. Unfortunately it turned out that the 4d mandelbrot set was just the normal one swept around the two new axes.

Now that I actually know how to program and it doesn't take hours to render an image it might be time to revisit this!

The Mandelbrot set is already 4-dimensional, sort of. It's called a Julibrot or Juliabrot fractal. In the definition of Mandelbrot and Julia sets (which use the same formula), Mandelbrot maps C to the output axes and Z starts at zero. For Julia, it's the other way around, but C is some constant rather than always zero, so there are lots of julia sets (although not all are interesting).

If you combine these and make both Z and C variables, you go from 2 dimensions to 4. If you count the escape iterations, that gives you 5.

This is basically the set of all Julia fractals, which also happens to contain the original Mandelbrot set across the hyperplane where Z=0.

Mobile-friendly view sort of works in Chrome.

The sections seem to be positioned absolutely with pixel offsets.. Ugh.

I never understood why mobile browsers don't allow you to force-scroll (and force-zoom out) to solve such issues.

Or just the real and imaginary axes?