Title: Getting derivative for plankton mandelbulbs etc.. Post by: mrrgu on December 28, 2009, 05:19:03 PM Hi
Ok I have been thinking about how to get the derivative for a plankton bulb.. I think the bulbs by cbuchner1 can be written as follows... Zn+1 = q2 * q1 * Zn^P * q2-1 * q1-1 + C There q1 q2 are rotation quaternions..like this qx = cos(ax/2)+ux*sin(ax/2) There ux are arbitrary axes...ax can be dependent on P ax=fx(P) or not.... Zn is a quaternion Zn=bi+cj+dk whus with a=0 ( q=a+bi+cj+dk ) Now it does not matter that Zn^P also causes rotations! what matters is that we add more rotations afterwards.. The rotations are independent of the derivative it would be.. DZn+1 = q2 * q1 * P * Zn^(P-1) * DZn * q1-1 * q2 -1 + 1 Thus same as before..just add rotations to it ;D I have not tested this yet.. but I think it will work.. Title: Re: Getting derivative for plankton mandelbulbs etc.. Post by: cbuchner1 on December 29, 2009, 08:02:34 PM I have recently bought Mathematica to crack this problem (among other things). But I am still learning how to use it - currently reading books like "Mathematicy Demystified". Title: Re: Getting derivative for plankton mandelbulbs etc.. Post by: mrrgu on December 31, 2009, 11:40:08 AM Ok, I tried it now.. It creates a blob rendered with good distance estimation. But I was wrong! adding rotations that are constant Is not what you do, It just destroy the fractality and smears things.. The rotations you do however are made by modfing an angle that that depends on previous angles..so there will be a derivative for each angle. A huge expression in the end :D |