3 ms·

I'm kind of worried that the images you are generating are just artifacts of your approach rather than getting at the fundamental nature of what is going on. T

by colomon 15y ago

I'm kind of worried that the images you are generating are just artifacts of your approach rather than getting at the fundamental nature of what is going on. The first thing that worries me is that your fractals don't look properly Mandelbrot-ish to my eye. Admittedly I've only ever looked at integer power Mandelbrot-like sets before, but all that I've ever looked at were either completely uninteresting or had snowmen somewhere. (I'm afraid I'm having a hard time putting into words what's bugging me, and alas I need to work, so I'm skipping what would be a much longer middle section to this post in an ideal world.) So I'd really like to see what happens if you make a particular branch choice and stick to that branch, for non-standard branches. And I'd like to see Julia sets. And I will try to get on implementing that stuff myself when I get the chance. :)

kens 15y ago
I understand what you're saying, My motivation is that I want to find the "fundamental nature" rather than artifacts or pretty pictures. The regular z^2.5+c fractal has obvious artifacts when you pass over the branch cut, and I hope that my technique is more "true". (These terms are all hard to define, but I think I mean the same thing you do.) I've explored different escape bounds, for instance, to make sure that isn't causing artifacts. (The bound causes huge artifacts with negative exponents, by the way.) It bothers me too that my fractals are less Mandelbrot-ish. I suspect this is due to all the branches overlapping and obscuring the details. I'm currently working on a couple ways to separate out these branches. Unfortunately just picking a different branch doesn't help, since it just moves the discontinuities. One plan is to display the fractal on the Riemann surface in 3D to separate the branches. The other plan is to crawl along the edge so you can continuously move from branch to branch without jumps. Julia sets are also on my list of things to do if I ever have time. If you do experiment with this, let me know what you find out.

by colomon 15y ago

kens 15y ago

I understand what you're saying, My motivation is that I want to find the "fundamental nature" rather than artifacts or pretty pictures. The regular z^2.5+c fractal has obvious artifacts when you pass over the branch cut, and I hope that my technique is more "true". (These terms are all hard to define, but I think I mean the same thing you do.) I've explored different escape bounds, for instance, to make sure that isn't causing artifacts. (The bound causes huge artifacts with negative exponents, by the way.) It bothers me too that my fractals are less Mandelbrot-ish. I suspect this is due to all the branches overlapping and obscuring the details. I'm currently working on a couple ways to separate out these branches. Unfortunately just picking a different branch doesn't help, since it just moves the discontinuities. One plan is to display the fractal on the Riemann surface in 3D to separate the branches. The other plan is to crawl along the edge so you can continuously move from branch to branch without jumps. Julia sets are also on my list of things to do if I ever have time. If you do experiment with this, let me know what you find out.