Sequences of symmetry-breaking in phyllotactic transitions |
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Authors: | Hiroyasu?Yamada Reiko?Tanaka Email author" target="_blank">Toshiyuki?NakagakiEmail author |
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Institution: | (1) Haruki-dai 5-1-2, Aichi 470-0161, Japan;(2) Department of Applied Physics and Physico-Informatics, Keio University, Yokohama 223-8522, Japan;(3) Creative Research Initiative “Sosei”, Research Institute for Electronic Science, Hokkaido University, Sapporo 060-0808, Japan |
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Abstract: | This paper studies the transition of phyllotactic patterns by a group-theoretic approach. Typical phyllotactic patterns are
represented here as dotted patterns on a cylinder, where the cylinder is regarded as the stem of a plant and the dots are
points where leaves branch from the stem. We can then classify the symmetries of the alternate and opposite phyllotaxis into
four types of groups, and clarify sequences of symmetry-breaking among these groups. The sequences turn out to correspond
to transition paths of phyllotactic patterns found in the wild. This result shows the usefulness of classification of phyllotactic
patterns based on their group symmetries. Moreover, the breaking of reflection symmetry is found to be an important rule for
real phyllotactic transitions. |
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Keywords: | |
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