2017年4月
Spiral disk packings
PHYSICA D-NONLINEAR PHENOMENA
- ,
- 巻
- 345
- 号
- 開始ページ
- 1
- 終了ページ
- 10
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1016/j.physd.2016.12.003
- 出版者・発行元
- ELSEVIER SCIENCE BV
It is shown that van Iterson's metric for disk packings, proposed in 1907 in the study of a centric model of spiral phyllotaxis, defines a bounded distance function in the plane. This metric is also related to the bifurcation of Voronoi tilings for logarithmic spiral lattices, through the continued fraction expansion of the divergence angle. The phase diagrams of disk packings and Voronoi things for logarithmic spirals are dual graphs to each other. This gives a rigorous proof that van Iterson's diagram in the centric model is connected and simply connected. It is a nonlinear analog of the duality between the phase diagrams for disk packings and Voronoi things on the linear lattices, having the modular group symmetry. (C) 2016 Elsevier B.V. All rights reserved.
- リンク情報
- ID情報
-
- DOI : 10.1016/j.physd.2016.12.003
- ISSN : 0167-2789
- eISSN : 1872-8022
- Web of Science ID : WOS:000395603000001