Title: Interesting Mandelbrot variant Post by: rollercoaster158 on June 12, 2012, 02:04:40 AM 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:
(http://i49.tinypic.com/2w3tb87.png) 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: (http://i45.tinypic.com/30m27fd.png) (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.) (http://i46.tinypic.com/23usegi.png) 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). (http://i49.tinypic.com/2w71e9k.png) That arrow is strange. I wonder how it is made by this formula. (http://i49.tinypic.com/v66s94.png) 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 Title: Re: Interesting Mandelbrot variant Post by: David Makin on June 12, 2012, 11:52:32 AM Erm, yes - most things have.
In this case to render it properly you need to increease the bailout - the magnitude of 2 proof is not valid for *any* formula. Here is what z^z+c looks like with a bailout of 256... http://www.fractalforums.com/index.php?action=gallery;sa=view;id=11782 (http://www.fractalforums.com/index.php?action=gallery;sa=view;id=11782) http://www.fractalforums.com/index.php?action=gallery;sa=view;id=11783 (http://www.fractalforums.com/index.php?action=gallery;sa=view;id=11783) http://www.fractalforums.com/index.php?action=gallery;sa=view;id=11784 (http://www.fractalforums.com/index.php?action=gallery;sa=view;id=11784) Params are with the 3rd image -- except that I also change the UF default z^p+c to do z^z+c so it'll only render corectly if you do the same ;) Of course anyone doing so needs to remember to change it back again after !! Title: Re: Interesting Mandelbrot variant Post by: DarkBeam on June 12, 2012, 12:32:41 PM Go to OPTIONS / UPDATE FORMULA COLLECTION :dink: There are millions of new formulas. Many made by the guy that answered your question :crazyeyes: in mmf-whatever :D
Mine are in lgn-whatever :dink: :police: You must use them everyday :snore: ;D Title: Re: Interesting Mandelbrot variant Post by: Alef on June 12, 2012, 06:39:46 PM If I 'm correct, this is one of classical fractints formulas. Probably should be in UF database in Fractint compatibility files.
Try EM files, too. And LKM (Or was they IKM :tongue1:) http://formulas.ultrafractal.com/ (http://formulas.ultrafractal.com/) Title: Re: Interesting Mandelbrot variant Post by: rollercoaster158 on June 13, 2012, 05:16:27 PM OK, it seems that I have a lot to learn about Ultrafractal. I just got it, and I'm still exploring the help files. Thanks for the help. |