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Author Topic: A 3-d function that has nearly spherical regions near the roots.  (Read 1156 times)
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msltoe
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Posts: 187


« 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:

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cKleinhuis
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« Reply #1 on: August 27, 2014, 12:48:41 AM »

huh? 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 ?
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divide and conquer - iterate and rule - chaos is No random!
msltoe
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Posts: 187


« Reply #2 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.
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DarkBeam
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« Reply #3 on: January 22, 2015, 12:55:15 PM »

Uhm looks nice!
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KRAFTWERK
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« Reply #4 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!!!
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