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WNdegree8quickexampleWhite/Nylander degree 5 Julia DE comparisonAnalytical DE
White/Nylander degree 5 Julia DE comparison
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Description: Created using Ultra Fractal.

A degree 5 White/Nylander Julia.

This shows that the difference in renders using the delta DE and analytical DE is sometimes not that great especially with a formula such as the White/Nylander where calculating the derivative is as complicated as calculating the normal iterate
The time differnce is not so great - note that how often the viewing rays approach the surface without striking it also has a bearing on the timing, this generally causes more slow down in the analytical method than the delta method.

You should note that the final DE calculation was modified to correct for scale differences for different powers/degrees, the UF calculation used (after trial and error based on getting the normals correct - the normals being calculated from adjacent DE values with no extra ray-tracing) was:

 dist = 0.5*sqrt(@mpwr-1.0)*log(magn)*sqrt(magn/(|dzri|+sqr(dzj)))

i.e. the usual calculation but scaled by the square root of the power/degree minus one.

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Filesize: 402.85kB
Height: 960 Width: 640
Keywords: true julia fractal digital algorithmic ultrafractal distance estimator 
Posted by: David Makin October 31, 2009, 03:50:54 AM

Rating: **** by 1 members.

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