FRACTAL DIMENSION, PRIMES, AND THE PERSISTENCE OF MEMORY
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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: the persistence of a number, and the memory of a prime. This similarity is quantified using fractal dimension.
1995 ◽
Vol 09
(12)
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pp. 1429-1451
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1999 ◽
Vol 29
(9)
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pp. 1301-1310
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