10/18/2022, 02:16 PM
(10/18/2022, 12:13 PM)Shanghai46 Wrote: This thread is especially addressed to Daniel, since the fractal down below is found on his tetration website.
So, how did you constructed it? What was the rules and exact definition you used? What's its fractal dimension, or other noticeable properties?
I think one of the major key to extend tetration is to study in detail this fractal, and other tetration fractals.
The fractal was constructed using FractInt, software developed on a CompuServe forum. I can still run the program in DosBox. UltraFractal runs FractInt formulas and also supports many fractals including the tetration escape fractal. The parameters are crazy - tens of thousands of iterations with a bailout 10^36. Note that I have two fractals on the front page of my website. The fractal you display is the period of different values; those values that don't escape. The other fractal is an classic escape fractal. Any software including Mathematica can generate escape fractals, but period identification is a difficult problem, although there are good algorithms for doing it. FractInt is the only software I'm aware of that supports period identification. More later.
Daniel