Symplastic growth of plant organs may be described by a continuous growth tensor field. In tensorial analysis of meristems, the trajectories of periclinal and anticlinal cell walls represent trajectories of the principal directions of growth (PDGs); this follows from the maintenance of mutual orthogonality between periclinal and anticlinal wall trajectories during growth. Periclinal and anticlinal cell divisions are also oriented in the principal planes of growth. The growth tensor for the root apex is specified in such a way that the principal directions of the tensor fit the pattern of periclinal and anticlinal walls in the apex, and that the grid formed by material particles aligned along PDG trajectories preserve this alignment during growth. Two growth tensors are formulated--one giving a maximum and the other giving a minimum of the volumetric relative elemental growth rate at the region of the initial cell(s). Temporal sequences of deformation of a grid formed by lines coinciding with the principal directions of growth are shown. The formation of cellular patterns in root apices is simulated. Two types of patterns are obtained: one with an apical cell and merophytes, and another with files of cells converging towards a quiescent centre.

中文翻译：

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差异生长导致根分生组织中不同类型的细胞结构的规范

植物器官的共生生长可以用连续生长张量场来描述。在分生组织的张量分析中，周和背斜细胞壁的轨迹代表生长主方向 (PDG) 的轨迹；这是由于在生长过程中保持了周斜和背斜壁轨迹之间的相互正交性。周和背斜细胞分裂也定向在生长的主要平面上。根尖的生长张量以这样的方式指定，即张量的主方向​​与根尖中的周壁和背斜壁的模式相匹配，并且由沿 PDG 轨迹排列的材料粒子形成的网格在生长过程中保持这种排列。公式化了两个生长张量——一个给出最大值，另一个给出初始细胞区域的体积相对元素生长速率的最小值。显示了由与主要生长方向重合的线形成的网格变形的时间序列。模拟根尖细胞模式的形成。获得两种类型的模式：一种具有顶端细胞和分生植物，另一种具有向静止中心会聚的细胞文件。