Mersenne Twister and Friends

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The Mathematica function SeedRandom comes with a variety of different methods: • "Sobol"—Sobol low-discrepancy sequence • "Niederreiter"—Niederreiter low-discrepancy sequence • "MCG31"—31-bit multiplicative congruential generator • "MCG59"—59-bit multiplicative congruential generator • "R250"—generalized feedback shift register generator • "WichmannHill"—Wichmann–Hill combined multiplicative congruential generators • "ExtendedCA"—extended cellular automaton generator (default) • "Rule30CA"—Wolfram rule 30 generator • "MersenneTwister"—Mersenne twister shift register generator • "MKL"—Intel MKL generator (Intel-based systems)

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There are two basic types, often identifiable by sight. The pseudorandom methods (such as the Mersenne Twister) seem random, while the quasirandom methods (such as Sobol) seem to have a pattern, with less clustering. As an example of where quasirandom methods might be better, one method for estimating the area of a shape is to bound it, then to pick random points from that area. Using pseudorandom numbers gives the Monte Carlo method. With quasirandom numbers, the method is called quasi-Monte Carlo. Due to the relative evenness of the quasirandom methods, sometimes they give better estimates.

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Contributed by: Ed Pegg Jr (March 2011)
Open content licensed under CC BY-NC-SA


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