Formation of square lattices in coupled pattern-forming systems

Authors

  • Christopher Strickland University of North Carolina-Chapel Hill and Statistical and Applied Mathematics Institute
  • Daniel A. Pearson Colorado State University
  • Patrick D. Shipman Colorado State University

DOI:

https://doi.org/10.11145/j.biomath.2016.12.181

Keywords:

pattern formation, phyllotaxis, nanoscale structures

Abstract

A wide variety of natural and labo-ratory systems can produce patterns of ripples, hexagons, or squares. The formation of stable square patterns from partial differential equation models requires specific cubic nonlinearities involving higher-order derivatives. Motivated by plant phyllotaxis, we demonstrate that the coupling of more than one pattern-forming system can produce square patterns without these special nonlinearities.

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Published

2017-01-17

Issue

Section

Original Articles