Construction of particle cellular automata models using the ultradiscretization method

我们已经成功地利用Max-Plus代数的规则表示法获得了四邻域粒子元胞自动机的通解。我们还成功地分析了通解的渐近行为。此外，我们还从基本图中得到了五邻域粒子元胞自动机的Max-Min-Plus表达式。得到了经超离散Cole-Hopf变换后的方程及其拉格朗日表示。利用极大极小格子，我们成功地得到了ECA的通解。

We have succeeded in obtaining the general solutions for four-neighborhood particle cellular automata using expression of rules in terms of Max-Plus algebra. We have also succeeded in analyzing asymptotic behavior of the general solutions. Furthermore, we have obtained Max-Min-Plus expressions for five-neighborhood particle cellular automata from fundamental diagrams. The equation transformed by ultradiscrete Cole-Hopf transformation and Lagrange representation of the equation are also obtained. We have succeeded in obtaining the general solutions of ECA using Max-Min lattice.