Sobol sequence

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)

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

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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