The Old Art of Rope Work and Fourier Decomposition

Nils Kr. Rossing
Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture (2012)
Pages 315–322 Regular papers

Abstract

Mathematically there is a close connection between pendulum drawing and rope mats. This article describes a method of analysing traditional rope mats and rosettes. By sampling the rope track one finds that the rope follows a periodic function both in x- and y-directions. Having the two periodic curves, it is possible to do a Fourier decomposition in both directions. By doing this the Fourier components are found for the two curves, or, as we may call it: The two-dimensional spectrum for the rosettes. By knowing the spectrum for some known mats and rosettes, it is possible to categorize the mats in families based on their order (number of needed components to represent the mat), which can be different from the traditional way of categorizing them. The Fourier components for the mats may now be used to synthesize the mat with a two-dimensional curve drawing software like Matlab or Winplot. By changing the Fourier components' frequency and amplitude, it is possible to make new variants of the mats and rosettes within the same family.

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