Phyllotaxis: a non-conventional crystalline solution to packing efficiency in situations with radial symmetry
Phyllotaxis: a non-conventional crystalline solution to packing efficiency in situations with radial symmetry
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DOI：
10.1107/s0108767312018910
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发表时间：
2012-07-01
影响因子：
1.8
通讯作者：
Charvolin, J.
中科院分区：
文献类型：
--
作者：
Sadoc, J-F;Rivier, N.;Charvolin, J.
叶序性是在一个大的圆形区域内寻找最均匀和最密集的小圆盘组织，最初是为了分析植物叶片或小花的排列。从那以后，它不仅成为植物学的研究对象，而且成为数学、计算机模拟和物理学的研究对象。虽然数学解决方案现在是众所周知的，一个算法设置的中心的小圆盘上的费马螺旋，这种组织的性质和它的性质的对称性仍有待审查。本文的目的是通过Voronoi细胞和Delaunay三角剖分来描述点的叶序组织，并参考凝聚态物理学中发展的缺陷概念。圆对称的拓扑约束引入了一种原始的膨胀-收缩对称性，取代了经典晶体学的平移和旋转对称性。
Phyllotaxis, the search for the most homogeneous and dense organizations of small discs inside a large circular domain, was first developed to analyse arrangements of leaves or florets in plants. It has since become an object of study not only in botany, but also in mathematics, computer simulations and physics. Although the mathematical solution is now well known, an algorithm setting out the centres of the small discs on a Fermat spiral, the very nature of this organization and its properties of symmetry remain to be examined. The purpose of this paper is to describe a phyllotactic organization of points through its Voronoi cells and Delaunay triangulation and to refer to the concept of defects developed in condensed matter physics. The topological constraint of circular symmetry introduces an original inflationdeflation symmetry taking the place of the translational and rotational symmetries of classical crystallography.