While messing around with my newly installed copy of Ultrafractal, I was editing the formula for the Mandelbrot set. Most of my variants were blank screens but then I came across a strange result. I changed the equation from Z=Z^2+C to Z=Z^Z+C. This was out of curiosity, to see what it would look like if the value Z was squared to was different for every pixel. Expecting a chaotic mix of different multibrots, I was surprised to see this:
I don't know if it's been discovered before, but a quick Google of the formula turns up nothing related to it. There are some interesting parts of this fractal, see for yourself:
(Yes, I did use MS Paint to label those. I have yet to obtain a decent image editing program so it will have to do. The following pictures are closeups of 1, 2, and 3 respectively.)
It does get a little chaotic, but I'm pleased with it. If you zoom in further, the mess settles out into mandelbrot-like spirals and shapes (sort of).
That arrow is strange. I wonder how it is made by this formula.
This is what the arrow is pointing at, there's nothing cool to see here. It goes on like that forever.
Anyway, here are my questions:
1. Has this been discovered before?
2. If the value that z is being multiplied by changes frequently, shouldn't there (theoretically) be a mini-brot of every value Z can be squared to in here?
3. Is there a way to make a 3d representation of this?
4. If it hasn't already been discovered, what would you name it? I have no idea what to call it.
rollercoaster158
November 26, 2009, 06:40:28 PM
A new 3d mandelbrot variant - Mandelcup
The 3D Mandelbulb
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