FRACTAL DIMENSION, PRIMES, AND THE PERSISTENCE OF MEMORY

Joseph L. Pe ()
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Joseph L. Pe: iDEN System Engineering Tools and Statistics, Motorola, 1501 W. Shure Drive, Atrium 5061 F33, Arlington Heights, IL 60004, USA

Advances in Complex Systems (ACS), 2003, vol. 06, issue 02, 241-249

Abstract: Many sequences from number theory, such as the primes, are defined by recursive procedures, often leading to complex local behavior, but also to graphical similarity on different scales — a property that can be analyzed by fractal dimension. This paper computes sample fractal dimensions from the graphs of some number-theoretic functions. It argues for the usefulness of empirical fractal dimension as a distinguishing characteristic of the graph. Also, it notes a remarkable similarity between two apparently unrelated sequences: thepersistenceof a number, and the memory of a prime. This similarity is quantified using fractal dimension.

Keywords: Empirical fractal dimension; number-theoretic functions; persistence of a number; memory of a prime; oscillator sequences (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1142/S0219525903000864

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