Editing Low-discrepancy sequence (section)

===Random numbers===

Sequences of quasirandom numbers can be generated from random numbers by imposing a negative correlation on those random numbers. One way to do this is to start with a set of random numbers <math>r_i</math> on <math>[0,0.5)</math> and construct quasirandom numbers <math>s_i</math> which are uniform on <math>[0,1)</math> using:

<math>s_i = r_i</math> for <math>i</math> odd and <math>s_i = 0.5 + r_i</math> for <math>i</math> even.

A second way to do it with the starting random numbers is to construct a random walk with offset 0.5 as in:

: <math>s_i = s_{i-1} + 0.5+ r_i \pmod 1. \, </math>

That is, take the previous quasirandom number, add 0.5 and the random number, and take the result [[modular arithmetic|modulo]]&nbsp;1.

For more than one dimension, [[Latin squares]] of the appropriate dimension can be used to provide offsets to ensure that the whole domain is covered evenly.

[[Image:Subrandom 2D.gif|thumb|270px|right|Coverage of the unit square. Left for additive quasirandom numbers with ''c''&nbsp;=&nbsp;0.5545497...,&nbsp;0.308517... Right for random numbers. From top to bottom. 10, 100, 1000, 10000 points.]]