  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.
