Title: A 3-d function that has nearly spherical regions near the roots. Post by: msltoe on August 27, 2014, 12:43:16 AM The function is
r=x*x+y*y+z*z x1 = (x*x-y*y)*(1-z*z/r) y1 = 2*x*y*(1-z*z/r) z1 = 2*z*sqrt(r) x=x1+a;y=y1+b;z=z1+c; The domain (r < threshold) is the spherical neighborhood of the root. You can color it completely (to make spherical roots) or you can do something more fancy like render torii: (http://nocache-nocookies.digitalgott.com/gallery/16/803_27_08_14_12_36_23.jpeg) Title: Re: A 3-d function that has nearly spherical regions near the roots. Post by: cKleinhuis on August 27, 2014, 12:48:41 AM ??? what is it, visually it looks like a julia set, how come the circles? by orbit trapping ?!
it seems to be a 3d function, how is it rendered by escape time 2d coloring or escape timed isosurfacing 3d ? Title: Re: A 3-d function that has nearly spherical regions near the roots. Post by: msltoe on August 27, 2014, 12:56:37 AM It's slightly different from true escape-time in that when r < threshold, I terminate the loop as I've now reached the neighborhood of a root.
The root is presumably at x=0,y=0,z=0. With that assumption I can draw things with respect to that origin. The torus, for example, is defined as points that are within a certain distance of a circle centered at the presumed origin. Title: Re: A 3-d function that has nearly spherical regions near the roots. Post by: DarkBeam on January 22, 2015, 12:55:15 PM Uhm looks nice!
Title: Re: A 3-d function that has nearly spherical regions near the roots. Post by: KRAFTWERK on January 22, 2015, 07:53:40 PM Uhm looks nice! Uhm, second that... great work as always msltoe! Looks lovely Back to compiling formulas Luca!!! |