What is the resolution of your original?
It's down-rezzed from 8400x6300, I think. The final two have stronger AA: computed at 16800x12600, I think.
Average iterations?
In the above image? A million or so. The final one is more impressive, probably nothing under 5 million and mostly over 10.
Is such a region not somewhat 'unattractive' due to the complexity/iteration ratio? And 94000000000 is also prohibitive for storing reference orbits unless one uses tricks (store one full period only).
Since perturbation wasn't used for this series, that was not an issue.
But this number could be reduced a lot without changing the image much, I guess.
I think there'd be a noticeable drop in quality with iteration limit of 100,000,000 and perhaps even higher. Probably a couple of billion would have sufficed, but I tend to err on the side of accuracy.
Are you using supercomputers?
That depends: is an AMD FX with six cores export-controlled and illegal to ship to Libya?
Nah, I used a speedup that I developed that's utterly orthogonal to perturbation (and so, could in principle be combined with it). One effect of the speedup is that if one is centered on a minibrot of period P, one can compute the image as accurately as by computing it conventionally with an iteration count of P*N while actually computing only about P+N iterations. Which for this period-94606 minibrot means that 94,606,000,000 iteration accuracy requires only about 1,100,000 actual iterations be computed.
It gets better. The 1,000,000 iterations are computed with hardware floating point, and the remaining up to 100,000 or so are computed at, in this case, only the precision normally needed at 10
103 magnification instead of 10
175. That's how this (and Mandelbrot Safari) could have the final minibrot images so accurate with only about three weeks per image instead of
years.
It's irked me just slightly that just as I was developing this method someone stole my thunder by producing the even more potent perturbation method.
November 02, 2011, 03:41:36 AM
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