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Low-discrepancy sequence
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==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 [[ACM Transactions on Mathematical Software|TOMS]] algorithm 659.<ref>{{cite journal|doi=10.1145/42288.214372|title=Algorithm 659 |year=1988 |last1=Bratley |first1=Paul |last2=Fox |first2=Bennett L. |journal=ACM Transactions on Mathematical Software |volume=14 |pages=88β100 |s2cid=17325779 |doi-access=free }}</ref> An implementation of the algorithm in [[Fortran]] is available from [[Netlib]]. {| style="border-spacing: 2px; border: 1px solid darkgray;" |- style="text-align: center;" | [[File:Low discrepancy 100.png|Low discrepancy 100.png]] | [[File:Low discrepancy 1000.png|Low discrepancy 1000.png]] |- style="text-align: center;" | The first 100 points in a low-discrepancy sequence of the [[Sobol sequence|Sobol']] type. | The first 1000 points in the same sequence. These 1000 comprise the first 100, with 900 more points. |} {| style="border-spacing: 2px; border: 1px solid darkgray;" |- style="text-align: center;" | [[File:Low discrepancy 10000.png|Low discrepancy 10000.png]] | [[File:Random 10000.png|Random 10000.png]] |- style="text-align: center;" | 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. |} {{Clear}}
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