Halton sequence
In statistics, Halton sequences are sequences used to generate points in space for numerical methods such as Monte Carlo simulations. Although these sequences are deterministic they are of low discrepancy, that is, appear to be random for many purposes. They were first introduced in 1960 and are an example of a quasi-random number sequence. They generalise the one-dimensional van der Corput sequences, consult that article for a precise definition.
Example of Halton sequence used to generate points in (0, 1) × (0, 1) in R2
The Halton sequence is constructed according to a deterministic method that uses a prime number as its base. As a simple example, let's take one dimension of the Halton sequence to be based on 2 and the other on 3. To generate the sequence for 2, we start by dividing the interval (0,1) in half, then in fourths, eighths, etc., which generates
and to generate the sequence for 3, we divide the interval (0,1) in thirds, then ninths, twenty-sevenths, etc., which generates
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