Quasi-Random Picture Gallery

The picture gallery exhibits typical applications of the Mathematica package QR Streams.

The first picture shows various plots of two-dimensional pseudo-random and quasi-random vectors. The quasi-random vectors are constructed from a variety of low-discrepancy sequences such as Halton, permuted Halton sequences and Niederreiter sequences in several different bases.

Every generator has the ability to draw samples from a specified distribution such as e.g. multinormal and extrem value distributions. In fact, every distribution known to Mathematica can be used directly with QR Streams.

In a last stage, mapped streams allow the transformation of a stream of pseudo- or quasi-random vectors, following any distribution.

This concept is visualized with various examples such as pseudo-random and quasi-random vectors (Niederreiter in base 3) on the disk, a disk with a hole and multinormally distributed quasi-random vectors, transformed with the complex ArcSin function.

The following QR Streams code example transforms a Niederreiter sequence in base 3, returning a stream object from which we can repetitively obtain quasi-random vectors on the disk. This is very convenient for numerical integration of functions on domains different than the unit cube.