Title: Non-trig expansion for RuckerBrot? Post by: DarkBeam on March 16, 2011, 12:40:48 PM Hi, I would like to ask to the geniuses of this wonderful forum: is there a non-trig expansion of the Rucker's MB3D?
Find the formula here: http://www.fractalforums.com/index.php?action=dlattach;topic=2081.0;attach=1031;image The entire topic http://www.fractalforums.com/theory/summary-of-3d-mandelbrot-set-formulas/ This is A Rucker PDF file with interesting explanations. http://www.rudyrucker.com/blog/notebooks/rucker_mandelbulb_ver7_sept24_2009.pdf Page 8 shows the non-trig expansion of White/Nylander formula (I hoped that was his formula!... :sad1: ) newx = ( x*x + y*y - z*z )*( x*x - y*y) / ( x*x + y*y ) newy = 2 * ( x*x + y*y - z*z )*x*y / ( x*x + y*y ) newz = - 2 * z * sqrt( x*x + y*y ) Thanks! Title: Re: Non-trig expansion for RuckerBrot? Post by: DarkBeam on March 16, 2011, 01:41:42 PM Hm. :hmh: Obtained this from WolframAlpha (x,y,z are real numbers so complex parts can be safely skipped), but still confused... cos(2 atan2(y,x) ) = +(y*y-x*x)/(y*y+x*x) sin(2 atan2(y,x) ) = -(4 y*z)/(y*y+x*x) then: cos(2 atan(z/x) ) = (x*x-z*z)/(z*z+x*x) sin(2 atan(z/x) ) = +(4 x*z)/(z*z+x*x) The strange thing is he says "atan(z/x)" and not 2*atan... cos(atan(z/x) ) = abs(x)/sqrt(z*z+x*x) sin(atan(z/x) ) = z/sqrt(z*z+x*x) * x/abs(x) What is correct? :o |