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arXiv · 1203.3837

Analysis of a Fivefold Symmetric Superposition of Plane Waves

Michael H. Schwarz·Robert A. Pelcovits
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Abstract

We show that a symmetric superposition of five standing plane waves can be expressed as an infinite series of terms of decreasing wavenumber, where each term is a product of five plane waves. We show that this series converges pointwise in R^2 and uniformly in any disk domain in R^2. Using this series, we provide a heuristic argument for why the locations of the local extrema of a symmetric superposition of five standing plane waves can be approximated by the vertices of a Penrose tiling.

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Michael H. Schwarz, Robert A. Pelcovits. 2012-03-17. Analysis of a Fivefold Symmetric Superposition of Plane Waves. https://arxiv.org/abs/1203.3837

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