Sobol sequence

Sobol’ sequences (also called LP_τ sequences or (t, s) sequences in base 2) are an example of quasi-random low-discrepancy sequences. They were first introduced by the Russian mathematician Ilya M. Sobol’ (Илья Меерович Соболь) in 1967.

256 points from the first 256 points for the 2,3 Sobol’ sequence (top) compared with a pseudorandom number source (bottom). The Sobol’ sequence covers the space more evenly. (red=1,..,10, blue=11,..,100, green=101,..,256)

These sequences use a base of two to form successively finer uniform partitions of the unit interval and then reorder the coordinates in each dimension.

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