User:Rob Formi/sandbox

Graphical examples

The points plotted below are the first 100, 1000, and 10000 elements in a sequence of the Sobol' type. For comparison, 10000 elements of a sequence of pseudorandom points are also shown. The low-discrepancy sequence was generated by TOMS algorithm 659.^[1] An implementation of the algorithm in Fortran is available from Netlib.

The first 100 points in a low-discrepancy sequence of the Sobol’ type.

The first 1000 points in the same sequence. These 1000 comprise the first 100, with 900 more points.

The first 10000 points in the same sequence. These 10000 comprise the first 1000, with 9000 more points.

For comparison, here are the first 10000 points in a sequence of uniformly distributed pseudorandom numbers. Regions of higher and lower density are evident.


The first 100 points in a low-discrepancy sequence of the Sobol' type.	The first 1000 points in the same sequence. These 1000 comprise the first 100, with 900 more points.


The first 10000 points in the same sequence. These 10000 comprise the first 1000, with 9000 more points.	For comparison, here are the first 10000 points in a sequence of uniformly distributed pseudorandom numbers. Regions of higher and lower density are evident.

^ Bratley, Paul; Fox, Bennett L. (1988). "Algorithm 659". ACM Transactions on Mathematical Software. 14: 88–100. doi:10.1145/42288.214372. S2CID 17325779.

[1] Bratley, Paul; Fox, Bennett L. (1988). "Algorithm 659". ACM Transactions on Mathematical Software. 14: 88–100. doi:10.1145/42288.214372. S2CID 17325779.

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