Document Type
Article
Publication Date
2019
Publication Title
Physica D: Nonlinear Phenomena
Abstract
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.
Keywords
Disk packing, Phyllotaxis, Rhombic tiling, Attractor, Dynamical system
DOI
doi.org/10.1016/j.physd.2019.132278
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Rights
*Published in Physica D, https://doi.org/10.1016/j.physd.2019.132278 ©2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Recommended Citation
Golé, Christophe and Douady, Stéphane, "Convergence in a Disk Stacking Model on the Cylinder" (2019). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/50
Comments
Peer reviewed accepted manuscript.