Vibration of the Koch drum A preprint version of a “ Mathematical graphics ” column from Mathematica in Education and Research

Abstract

The Koch snowflake is a well known self-similar set whose boundary is a fractal curve. Suppose a vibrating membrane with fixed boundary, i.e. a drum, is shaped like a Koch snowflake. The fundamental modes of vibration of this drum can be modelled by the eigenfunctions of the Laplacian on the snowflake. These, in turn, can be approximated by a discrete… (More)

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