buddhabrot montecarlo and quasi-montecarlo

[knighty]

After having read an article about quasi-montecarlo methods, I gave it a try with the buddhabrot by using Halton sequences instead of pseudo-random numbers. It appears that the former converges faster w.r.t. the number of samples. That's for the good news. The bad news are that it is much slower in practice probably because it is very cache unfriendly. One solution to this problem I could find is to divide the sampling area into a grid then scanning it and using Halton sequence as a perturbation.
For comparison here are the results for 128, 512 and 1000 iterations with 100000 samples each:
Halton-128:

rnd-128:

Halton-512:

rnd-512

Halton-1000:

rnd-1000:


Here is also an evaldraw script showing both approaches at the same time (top half: Halton. bottom half: pseudo random)

[matsoljare]

They might be a good choice for the "Supermandelbrot" rendering i pioneered myself, as well...

[Alef]

Could someone explain haltonian sequences using some simple c like pseudocode for those who don't have Borland C instaled and would like to make this in Ultra Fractal;)
This is pretty usefull stuff for a buddhabrot like. This Quasi Random numbers in certain application seems to be much superiour over random number genertors. But maybe they could be multiplied to create halton-random sequences. Anyway, downloaded lots of .pdf about halton sequences.

[Roquen]

http://www.cs.cmu.edu/~ajw/s2007/IncrementalHalton.cpp