Formation of square lattices in coupled pattern-forming systems

Christopher Strickland, Daniel A. Pearson, Patrick D. Shipman

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.

Keywords


pattern formation; phyllotaxis; nanoscale structures

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DOI: http://dx.doi.org/10.11145/j.biomath.2016.12.181

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ISSN 1314-7218 (online)
ISSNĀ 1314-684X (print)

Indexed by: Mathematical Reviews, Zentralblatt MATH, EBSCO, Google Scholar