Archimedean Voronoi spiral tilings
Archimedean Voronoi spiral tilings
复制标题
阿基米德沃罗诺伊螺旋瓷砖
DOI：
10.1088/1751-8121/aa9ada
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Yoshikazu Yamagishi and Takamichi Sushida
中科院分区：
文献类型：
--
作者：
Long;Hongwei.; Ma;Chunhua. and Shimizu;Yasutaka.;Yoshikazu Yamagishi and Takamichi Sushida
我们研究了阿基米德螺旋晶格的Voronoi平铺内的螺旋（称为parastichy在phyllotaxis理论）的数量的过渡。在一个镶嵌内的局部parastichy数的过渡被认为是一个连续的家庭的镶嵌在基地点的过渡。这给出了晶界的准周期结构的自然描述。证明了晶界上的瓦片数是生成元辐角（称为发散角）的有理逼近因子。局部寄生数是塑时参数的非减函数。局部parastichy数的分支图具有Farey树结构。
We study the transition of the number of spirals (called parastichy in the theory of phyllotaxis) within a Voronoi tiling for Archimedean spiral lattices. The transition of local parastichy numbers within a tiling is regarded as a transition at the base site point in a continuous family of tilings. This gives a natural description of the quasiperiodic structure of the grain boundaries. It is proved that the number of tiles in the grain boundaries are denominators of rational approximations of the argument (called the divergence angle) of the generator. The local parastichy numbers are non-decreasing functions of the plastochron parameter. The bifurcation diagram of local parastichy numbers has a Farey tree structure.