Coastlines violate the Schramm–Loewner Evolution

Leidy M.L. Abril, Erneson A. Oliveira, André A. Moreira, José S. Andrade and Hans J. Herrmann

Physica A: Statistical Mechanics and its Applications, 2024, vol. 653, issue C

Abstract: Mandelbrot’s empirical observation that the coast of Britain is fractal has been confirmed by many authors, but it can be described by the Schramm–Loewner Evolution? Since the self-affine surface of our planet has a positive Hurst exponent, one would not expect a priori any critical behavior. Here, we investigate numerically the roughness and fractal dimension of the isoheight lines of real and artificial landscapes. Using a novel algorithm to take into account overhangs, we find that the roughness exponent of isoheight lines is consistent with unity regardless of the Hurst exponent of the rough surface. Moreover, the effective fractal dimension of the iso-height lines decays linearly with the Hurst exponent of the surface. We perform several tests to verify if the complete and accessible perimeters would follow the Schramm–Loewner Evolution and find that the left passage probability test is clearly violated, implying that coastlines violate SLE.

Keywords: Coastlines; Local width; Fractal dimension; SLE theory; Self-similarity; Conformal theory (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:653:y:2024:i:c:s0378437124005752

DOI: 10.1016/j.physa.2024.130066

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