Created using Ultra Fractal.
Changed the rendering algorithm to a much simpler distance estimation method : a = a + sqrt(|z|/|dz|)
Same image, rendered at 2048*1536 again : time 9mins 4secs
Much fewer errors and plenty scope for minor changes to give a perfect render given the render speed
Previous versions:
[link]
[link]
Changed the rendering algorithm to a much simpler distance estimation method : a = a + sqrt(|z|/|dz|)
Same image, rendered at 2048*1536 again : time 9mins 4secs
Much fewer errors and plenty scope for minor changes to give a perfect render given the render speed
Previous versions:
[link]
[link]
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Actually it seems all I've found is the path to the derivation of the standard distance estimator method that Ron Barnett's Raytracing formulas use.
My method was based on using the Newton to solve equations for the step distance based on the bailout values directly, I realised that it would be better to use the smooth iteration value rather than using the bailout value and in trying that discovered that that is the derivation of the standard distance estimator method
I seem to have a talent for re-inventing the wheel - but it's always nice to have a complete understanding of such things and that always comes best from doing it yourself
Anyway I think I now know how to do a good combination of "brute force" and distance estimator to bring the times down for the non-standard 4D maths fractals without having to find the analytical derivative - it would still make rendering them slower than using the full DE but should make them a lot faster and more accurate than my original iteration density method.