The Beautiful Fractal

[M Benesi]

  This formula is simply phenomenal.  Its coloring emerges with complete simplicity and indicates exactly where locations of activity are present.  It has the infinite variety of the 2d Mandelbrot when zooming into spots.  z^2?  Awesome.  You can zoom into many different locations and find tons of variations and fractal patterns.  z^3+?  Same thing.  It produces interesting patterns for all of them.

  Anyways, a few first images of the brand new type.  Later, I'll do a zoom into a portion of the z^2.  Already checked out the stalk: beautiful crystalline structures abound (but have no great images as of yet).

Straight on z^2:
 
top down z^2:

front (optical illusion, it's and outie that looks like an innie) z^2:

rear z^2:


Some other z^n fronts:
z^4:

z^8:


and a z^8 rear:

[twinbee]

That colouring looks interesting. Can you use it on the Mandelbulb power apx 8 to see how it looks there?