Yamada Hiroyasu, Tanaka Reiko, Nakagaki Toshiyuki
Department of Applied Physics and Physico-Informatics, Keio University, Yokohama, Japan.
Bull Math Biol. 2004 Jul;66(4):779-89. doi: 10.1016/j.bulm.2003.10.006.
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.
本文采用群论方法研究叶序模式的转变。这里将典型的叶序模式表示为圆柱上的点状模式，其中圆柱被视为植物的茎，点则是叶子从茎上分支的位置。然后，我们可以将互生叶序和对生叶序的对称性分为四类群，并阐明这些群之间的对称破缺序列。结果表明，这些序列与在自然中发现的叶序模式转变路径相对应。这一结果显示了基于群对称性对叶序模式进行分类的有用性。此外，发现反射对称性的破缺是实际叶序转变的一个重要规则。
