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Analytical DEDelta DE final testDelta DE - testing the limits
Delta DE final test
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Description: I confess the previous render took so long because I had an issue with the shadow-casting and to fix it I ended up increasing the "accuracy" setting to 10 - thus reducing all step sizes to one tenth of the default, hence it took so long.
However I've fixed that and also discovered that the other errors (the scalloping and edge inaccuracy) where scalable erors such that going closer to the "solid" also reduced the size of the errors, making them almost unnoticeable.
This render took under 11 minutes at 640*480 and used the following settings:

Magnification: 2.1582312 e12
Solid threshold: 1 e-14
Delta: 1.25 e-15

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Total Favorities: 0 View Who Favorited
Filesize: 385.31kB
Height: 480 Width: 640
Keywords: quaternion mandelbrot fractal deep zoom ultrafractal 
Posted by: David Makin October 22, 2009, 04:20:02 AM

Rating: ***** by 1 members.

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David Makin
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October 23, 2009, 08:05:49 PM
Am working on it.
I've added the analytical DE method for quaternions to my WIP formula and tried rendering this using that method, I gave up on it after one whole minute passed with 0 pixels completed !
Further investigation reveals that at larger solid thresholds the analytical method is faster and more accurate than the delta DE (numerical) method but as the solid threshold is reduced the delta DE method becomes optimum.
For a solid threshold of down to around 5e-4 the analytical method is probably better but by 5e-5 the delta DE method is faster and by 1e-5 it's probably time to give up on the analytical method altogether smiley

Edit: Just found an issue in my WIP formula that explained why the analytical method was so slooowww and fixed it. Now the analytical method is as quick or quicker and more accurate - as I expected it should have been in the first place smiley
Buddhi
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October 23, 2009, 04:08:10 PM
Interesting experiment and amusing results. I'm waiting for some renderings with high details deep zooms of 3D fractals or some deep zoom animation.

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