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arXiv · 1707.06225

Waves along fractal coastlines: From fractal arithmetic to wave equations

Marek Czachor
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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.

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Marek Czachor. 2017-07-18. Waves along fractal coastlines: From fractal arithmetic to wave equations. https://doi.org/10.5506/aphyspolb.50.813

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