Formation of square lattices in coupled pattern-forming systems

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