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Thornton Degree 2 XZ sliceThornton Degree 2 XY SliceThornton Degree 2 Full
Thornton Degree 2 XY Slice
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Description: Created using Ultra Fractal.

This is a render of the degree 2 version of the formula suggested by Garth Thornton based on the formula due to Daniel White and Paul Nylander.

Here's the iteration loop as used in UF (note that the initial value of magn is pre-calculated):

          if magn<1e-200
            zri = cri
            zj = cj
          else
            r = (magn=sqrt(magn))^@mpwr
            th = @mpwr*atan2(zri)
            ph = @mpwr*acos(zj/magn);(real(zri)+flip(zj));
            zri = r*(cos(th)*sin(ph) + flip(sin(ph)*sin(th))) + cri
            zj = r*cos(ph) + cj
          endif
          magn = |zri| + sqr(zj)

Anyone wanting more information on these investigations into 3D fractals should go here:

http://www.fractalforums.com/3d-fractal-generation/true-3d-mandlebrot-type-fractal/

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Filesize: 175.81kB
Height: 480 Width: 640
Keywords: mandelbrot fractal algorithmic digital ultrafractal 
Posted by: David Makin October 12, 2009, 12:09:17 AM

Rating: ***** by 1 members.

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