Waves along fractal coastlines: From fractal arithmetic to wave equations

Abstract

Beginning with addition and multiplication which are intrinsic to a Koch-type curve, I formulate and solve a wave equation that describes wave propagation along a fractal coastline. As opposed to the examples known from the literature I do not replace the fractal by the continuum in which it is embedded. This seems to be the first example of a truly intrinsic description of wave propagation along a fractal curve.

First version of the paper was submitted to arXiv on 9 Jul 2017

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• Unifying Aspects of Generalized Calculus
• Arithmetic loophole in Bell's theorem: An overlooked threat to entangled-state quantum cryptography
• Non-Newtonian mathematics instead of non-Newtonian physics: Dark matter and dark energy from a mismatch of arithmetics
• A loophole of all `loophole-free' Bell-type theorems
• Imitating quantum probabilities: Beyond Bell's theorem and Tsirelson bounds
• On the Relativity of Quantumness as Implied by Relativity of Arithmetic and Probability
• Contra Bellum: Bell's theorem as a confusion of languages