Proving the deterministic period breaking of linear congruential generators using two tile quasicrystals

Guimond, Louis-Sébastien; Patera, Jiří

doi:10.1090/S0025-5718-01-01331-X

Proving the deterministic period breaking of linear congruential generators using two tile quasicrystals
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by Louis-Sébastien Guimond and Jiří Patera;

Math. Comp. 71 (2002), 319-332

DOI: https://doi.org/10.1090/S0025-5718-01-01331-X

Published electronically: September 17, 2001

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Abstract:

We describe the design of a family of aperiodic PRNGs (APRNGs). We show how a one-dimensional two tile cut and project quasicrystal (2TQC) used in conjunction with LCGs in an APRNG generates an infinite aperiodic pseudorandom sequence. In the suggested design, any 2TQC corresponding to unitary quadratic Pisot number combined with either one or two different LCGs can be used.

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