Fractal surfaces from simple arithmetic operations

Abstract

Fractal surfaces ('patchwork quilts') are shown to arise under most general circumstances involving simple bitwise operations between real numbers. A theory is presented for all deterministic bitwise operations on a finite alphabet. It is shown that these models give rise to a roughness exponent $H$ that shapes the resulting spatial patterns, larger values of the exponent leading to coarser surfaces.

15 pages, 6 figures, minor corrections. Published in Physica A

References in corpus (1)

• The $p\lambda n$ fractal decomposition: Nontrivial partitions of conserved physical quantities

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