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Illustration of a low-discrepancy sequence
Here is an illustration of a low-discrepancy sequence.
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, described by P. Bratley and B.L. Fox in ACM Transactions on Mathematical Software, vol. 14, no. 1, pp 88--100. An implementation of the algorithm in Fortran may be downloaded from Netlib, URL: http://www.netlib.org/toms/659
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.
10-26-2009 08:16:03
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details