Mersenne Twister and Friends

randomness method

MersenneTwister

random seed

number of points

The Mathematica function SeedRandom for generating pseudorandom or quasirandom numbers 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)

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.

Details

Using the plastic constant for quasirandom sequences was suggested in[1]. The supergolden ratio also works.

References

[1] Martin Roberts, Evenly Distributing Points in a Triangle.

External Links

Quasirandom Number (Wolfram MathWorld)

Plastic Constant (Wolfram MathWorld)

Pseudorandom Number (Wolfram MathWorld)

Random Number (Wolfram MathWorld)

Random Number Generation (Wolfram Documentation Center)

SeedRandom (Wolfram Documentation Center)

Permanent Citation

Ed Pegg Jr

"Mersenne Twister and Friends"
http://demonstrations.wolfram.com/MersenneTwisterAndFriends/
Wolfram Demonstrations Project
Published: March 7, 2011