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Thornton Degree 2 XZ 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: 120.72kB
Height: 480 Width: 640
Keywords: mandelbrot fractal digital algorithmic ultrafractal
Posted by: David Makin October 12, 2009, 12:10:20 AM

Rating: by 1 members.