Title: Perfect 3d Mandelbrot Post by: M Benesi on June 17, 2010, 09:19:52 PM Hey all, posted it in the 3d Fractal Generation subforum (http://www.fractalforums.com/3d-fractal-generation/true-3d-mandelbrot-finally/msg18386/#msg18386), but just to show you, this is the 3d Mandelbrot. Here are some boring, straight on, z^5 slices (that look exactly like a z^5 2d Mandelbrot). They are the same over all axes. looking down (towards negative) y axis: (http://lh5.ggpht.com/_gbC_B2NkUEo/TBpvX-_LiDI/AAAAAAAAAZ0/7ciNifsyDXM/facing%20neg%20y.jpg) looking down the z: (http://lh4.ggpht.com/_gbC_B2NkUEo/TBpvX7ry9jI/AAAAAAAAAZ4/HOnluBxxAgk/facing%20neg%20z.jpg) lookin' down x: (http://lh3.ggpht.com/_gbC_B2NkUEo/TBpvX-apIzI/AAAAAAAAAZ8/4YO9VzdmxEE/facing%20towards%20negative%20x.jpg) Basically, for the 'type I' 3d Mandelbrot fractal, there is only complete symmetry every 4th z^n (z^5, z^9, z^13....). It's the version I created "Ghost Lord" with, just did the slices today. I mentioned some stuff about the symmetry in the other thread, and maybe someone else will come up with some ideas, maybe David can make a nice delta-DE method if he feels like doing the math. Anyways, it exists, and it's fractal in a bunch of z^n. The 3d version is symmetric every 4th, the 2d every 2nd... so the 4d might be every 8th (should do the formula and check later, stuff to do now). Have fun. |