Pretty pictures II
I said I'd keep messing with it! I developed a weird non-associative (?), non-commutative algebra, then tried mapping it onto 3 dimensions and... well, whether or not I did it right, I finally came up with something interesting:
Transverse plane moving bottom-to-top.
Preliminary 3D rendering.
In examining the 3D model, I discovered that the fractal does actually have a plane of symmetry, along which the original Mandelbrot set (albeit a tiny bit distorted) appears:
Plane of symmetry traveling along normal.
Note, even though the Mandelbrot seems to just "flash" in this animation, it does not appear instantaneously, but rather "fades in" very rapidly:
Same as above with logarithmic time scale.
Transverse plane moving bottom-to-top.
Preliminary 3D rendering.
In examining the 3D model, I discovered that the fractal does actually have a plane of symmetry, along which the original Mandelbrot set (albeit a tiny bit distorted) appears:
Plane of symmetry traveling along normal.
Note, even though the Mandelbrot seems to just "flash" in this animation, it does not appear instantaneously, but rather "fades in" very rapidly:
Same as above with logarithmic time scale.