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.