Illustration of a low-discrepancy sequence

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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

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Image:Low discrepancy 100.png

Image:Low discrepancy 1000.png

Image:Low discrepancy 10000.png

Image:Random 10000.png