我们研究了概率性全总型元胞自动机的平均场表述逼近逻辑斯蒂方程的条件。结果表明，该目标仅在无限范围邻域下才能实现。我们数值研究了相应的二维一维实现，发现通过在每个时间步对配置进行随机重排，或以类似“小世界”机制的方式，在每个时间步重连部分连接，或仅一次性使用相同的随机采样进行重连，均可使平均场描述趋于成立。我们证明，即使重连连接的比例小于1，也能获得对逻辑斯蒂行为的良好近似。此外，我们还发现密度随重连比例变化呈现出分岔级联现象，且这一现象在具有与概率型元胞自动机相同基本对称性的确定性全总型元胞自动机中同样成立。

We investigate the conditions under which the mean-field formulation of a probabilistic, totalistic cellular automaton approximates the logistic equation. We show that this goal can be only fulfilled for an infinite-range neighborhood. We numerically study the corresponding one-dimensional implementation, showing that the mean-field description is obviously approached by shuffling the configuration at each time step, but also by rewiring a fraction of links, either at each time step, or using the same random sampling once and for all, in the spirit of the "small-world" mechanism. We show that it is possible to obtain a good approximation of the logistic behavior already with a fraction of rewired links different from one. We also show that there is a bifurcation cascade of the density as a function of the fraction of the rewired links, and that this scenario also holds for a deterministic, totalistic CA with the same basic symmetries of the probabilistic one.