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Analyzing Logistic Map Pseudorandom Number Generators For Periodicity Induced By Finite Precision Floating-Point Representation, Kyle Persohn, Richard J. Povinelli

Electrical and Computer Engineering Faculty Research and Publications

Because of the mixing and aperiodic properties of chaotic maps, such maps have been used as the basis for pseudorandom number generators (PRNGs). However, when implemented on a finite precision computer, chaotic maps have finite and periodic orbits. This manuscript explores the consequences finite precision has on the periodicity of a PRNG based on the logistic map. A comparison is made with conventional methods of generating pseudorandom numbers. The approach used to determine the number, delay, and period of the orbits of the logistic map at varying degrees of precision (3 to 23 bits) is described in detail, including the …