我们研究了采用多数表决或受挫多数表决规则、且相互作用范围可变的布尔型全同型细胞自动机。这两个模型的行为均偏离平均场行为。多数表决模型具有吸收态,其相变行为随初始密度变化,与平均场近似结果一致;但当初始密度为0.5时,系统动力学由粗化过程主导,该过程在形成具有确定曲率半径的团簇后停止。对于受挫多数表决模型,平均场近似预测混沌振荡或极限环,而我们实际观察到的是具有稳定密度的活性图案;当相互作用半径超过某一临界值时,渐近密度随初始密度变化出现分岔。
We investigate Boolean, totalistic cellular automata with a majority or frustrated majority vote rule, and an interaction range of variable span. These two models show a behavior which differs from the mean-field one. The majority vote model is characterized by the presence of absorbing states, and there is a related bifurcation according to the initial density, in agreement with the mean-field approximation. For initial density equal to $0.5$, however, the dynamics is dominated by a coarsening process, which stops when clusters with a definite curvature radius are established. For the frustrated majority vote model, the mean-field approximation gives chaotic oscillations or a limit cycle. Instead, we observe active patterns, with stable density. Above a certain critical value for the interacting radius there is a bifurcation of the asymptotic density as a function of the initial one.