The Unreasonable Effectiveness
of Quasirandom Sequences

I present a new low discrepancy quasirandom sequence that offers many substantial improvements over other popular sequences such as the Sobol and Halton sequences.

Figure 1a. Comparison of the various low discrepancy quasirandom sequences. Note that the newly proposed $R$-sequence produces more evenly spaced points than any of the other methods. Furthermore, all other current methods require careful selection of basis parameters, and if not chosen carefully can lead to degeneracy (eg top right).

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A simple method to construct isotropic quasirandom
blue noise point sequences

I describe a simple method for constructing a sequence of points, that is based on a low discrepancy quasirandom sequence but exhibits enhanced isotropic blue noise properties. This results in fast convergence rates with minimal aliasing artifacts.

Figure 1. The first 100, 200, 500, 1000, 2000 and 5000 sample points of the proposed point sequence (eqn 11) that is progressive, non-stochastic, exhibits near isotropic blue noise characteristics with fast QMC convergence rates with reduced artifacts. It is based on a new simple low discrepancy quasirandom sequence, $R_2$.

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