Wang Daimu, Sun Xia, Wu Ziqin
Department of Astronomy and Applied Physics, University of Science and Technology of China, Hefei 230026, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Oct;68(4 Pt 2):047104. doi: 10.1103/PhysRevE.68.047104. Epub 2003 Oct 29.
A helical cellular automata (HCA) model constructed on a two-dimensional grid of cells with a helical structure is presented and the pattern formation of this model studied by numerous computer simulations. It is found that the evolutions of the HCA are sensitive to the circumference of the helix p. With various p, the initial growth of the model generates various patterns ranging from Sierpinski triangle gasket, complex textured pattern, to lateral quasiperiodic structure. A sudden transition from regular fractal to compact pattern occurs near the point where p is equal to a positive integer power of 2. With increasing height of the patterns (increasing growth time), the model also exhibits different growth behaviors in the vertical direction for various p, including the formation of regular periodic patterns and the evolution from initial regular patterns to eventual random structures. Fractal dimension analysis is used to characterize these different evolution processes quantitatively.
提出了一种基于具有螺旋结构的二维细胞网格构建的螺旋细胞自动机（HCA）模型，并通过大量计算机模拟研究了该模型的图案形成。发现HCA的演化对螺旋周长p敏感。对于不同的p，模型的初始生长产生各种图案，从谢尔宾斯基三角形垫片、复杂纹理图案到横向准周期结构。在p等于2的正整数幂的点附近，会发生从规则分形到紧凑图案的突然转变。随着图案高度的增加（生长时间增加），对于不同的p，模型在垂直方向上也表现出不同的生长行为，包括规则周期图案的形成以及从初始规则图案到最终随机结构的演化。使用分形维数分析对这些不同的演化过程进行定量表征。
