Convergence in a disk stacking model on the cylinder

PHYSICA D-NONLINEAR PHENOMENA

卷:403

Article

Gole, Christophe¹  Douady, Stephane² 

[1] Smith Coll, Math & Stat Dept, Northampton, MA 01063 USA

[2] CNRS, Lab Matiere & Syst Complexes, Paris, France

关键词: Disk packing;    Phyllotaxis;    Rhombic tiling;    Attractor;    Dynamical system;   

DOI  :  10.1016/j.physd.2019.132278

来源: Elsevier

【 摘 要 】

We study an iterative process modeling growth of phyllotactic patterns, wherein disks are added one by one on the surface of a cylinder, on top of an existing set of disks, as low as possible and without overlap. Numerical simulations show that the steady states of the system are spatially periodic, lattices-like structures called rhombic tilings. We present a rigorous analysis of the dynamics of all configurations starting with closed chains of 3 tangent, non-overlapping disks encircling the cylinder. We show that all these configurations indeed converge to rhombic tilings. Surprisingly, we show that convergence can occur in either finitely or infinitely many iterations. The infinite-time convergence is explained by a conserved quantity. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free