Waves along fractal coastlines: From fractal arithmetic to wave equations
Dynamical Systems
2019-04-11 v2 Mathematical Physics
math.MP
Chaotic Dynamics
Pattern Formation and Solitons
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.
Keywords
Cite
@article{arxiv.1707.06225,
title = {Waves along fractal coastlines: From fractal arithmetic to wave equations},
author = {Marek Czachor},
journal= {arXiv preprint arXiv:1707.06225},
year = {2019}
}
Comments
First version of the paper was submitted to arXiv on 9 Jul 2017