Title: Adding some imagination... Post by: David Makin on December 04, 2009, 11:50:24 PM Here are two renders of the Mandelbulb extended to complex "power" - (6,1) in this case.
I checked the XY slices and they unfortunately do not match the complex z^(6,1) + c Mandelbrot - the "bottom" looks correct but the bulbs are missing off the top - looking at the renders it looks like they're displaced in z on the Mandelbulb. In the formulas note that ztemp, zri, cri and @power are complex and the rest are real. Also |zri| is x^2+y^2 where zri = (x+i*y). "-sine version": if (r = |zri|)>0.0 ztemp = ((r=sqrt(r)) + flip(zj))^@power zri = real(ztemp)*(zri/r)^@power + cri zj = cj - imag(ztemp) else zri = cri zj = cj - imag(flip(zj)^@power) endif (http://www.fractalforums.com/gallery/1/141_04_12_09_11_40_39.png) "+sine" version if (r = |zri|)>0.0 ztemp = ((r=sqrt(r)) + flip(zj))^@power zri = real(ztemp)*(zri/r)^@power + cri zj = cj + imag(ztemp) else zri = cri zj = cj + imag(flip(zj)^@power) endif (http://www.fractalforums.com/gallery/1/141_04_12_09_11_42_36.png) Title: Re: Adding some imagination... Post by: David Makin on December 05, 2009, 12:02:05 AM Regarding: if (r = |zri|)>0.0 ztemp = ((r=sqrt(r)) + flip(zj))^@power zri = real(ztemp)*(zri/r)^@power + cri zj = cj - imag(ztemp) else zri = cri zj = cj - imag(flip(zj)^@power) endif I've assumed the zri/r is zero if |zri| is zero, would it be better to assume it is (1,0) instead ? I did try it in the remote chance it would fix the XY cross-sections but it made no difference at all to the renders. |