Shape Limit in Triangular Spiral Tilings

• Authors: T. Sushida , A. Hizume , Y. Yamagishi
• Languages of publication: EN

Abstracts

EN

Phyllotaxis is the study of arrangements of leafs and florets. The topology of triangular spiral (multiple) tilings with opposed parastichy pairs is intimately related to the phyllotaxis theory and continued fractions. It is shown that, if the divergence angle of the genetic spiral is given as a quadratic irrational and fixed, then the limit set of the shape parameters of triangular tiles, as the parastichy numbers tend to infinity, is a finite set. In particular, the limit is the golden section if the divergence angle is `ultimately golden'.

Keywords

EN

02.10.De; 02.30.Oz; 02.40.Pc; 87.10.Hk

Discipline

• 02.10.De: Algebraic structures and number theory
• 87.10.Hk: Lattice models
• 02.40.Pc: General topology
• 02.30.Oz: Bifurcation theory(see also 47.20.Ky in fluid dynamics)

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2014
• Volume: 126
• Issue: 2
• Pages: 633-636

Dates

published

2014-08

Contributors

author

T. Sushida

• Department of Applied Mathematics and Informatics, Ryukoku University, Seta, Otsu, 520-2194 Japan

author

A. Hizume

• Department of Applied Mathematics and Informatics, Ryukoku University, Seta, Otsu, 520-2194 Japan

author

Y. Yamagishi

• Department of Applied Mathematics and Informatics, Ryukoku University, Seta, Otsu, 520-2194 Japan

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Identifiers

DOI

10.12693/APhysPolA.126.633