We study qualitative properties of two-dimensional freezing cellular automata with a binary state set initialized on a random configuration. If the automaton is also monotone, the setting is equivalent to bootstrap percolation. We explore the extent to which monotonicity constrains the possible asymptotic dynamics by proving two results that do not hold in the subclass of monotone automata. First, it is undecidable whether the automaton almost surely fills the space when initialized on a Bernoulli random configuration with density $p$, for some/all $0 < p < 1$. Second, there exists an automaton whose space-filling property depends on $p$ in a non-monotone way.
翻译:我们用随机配置的二维冻结细胞自动成像状态来研究二维冻结细胞自动成像的定性特性。 如果自动成像也是单质的, 设置就相当于靴带穿孔。 我们通过证明单质性能在单质自动成像小类中不持有两种结果来探索单质约束可能的无症状动态的程度。 首先, 自动成像是否在以密度为$/ 全部 $ < p < 1 美分的伯努利随机配置中几乎肯定填满了空间, 以非单质方式, 其空间填充属性取决于$p美元 。