For non-uniform cellular automata (NUCA) with finite memory over an arbitrary
universe with multiple local transition rules, we show that pointwise
nilpotency, pointwise periodicity, and pointwise eventual periodicity
properties are respectively equivalent to nilpotency, periodicity, and eventual
periodicity. Moreover, we prove that every linear NUCA which satisfies
pointwise a polynomial equation (which may depend on the configuration) must be
an eventually periodic linear NUCA. Generalizing results for higher dimensional
group and linear CA, we also establish the decidability results of the above
dynamical properties as well as the injectivity for arbitrary NUCA with finite
memory which are local perturbations of higher dimensional linear and group CA.
Some generalizations to the case of sparse global perturbations of higher
dimensional linear and group CA are also obtained.

研究非均匀细胞自动机的特性，证明了点状幂零、周期性和最终周期性等性质与幂零、周期性和最终周期性等性质分别等价。此外，还证明了每个满足点方程（可能依赖于配置）的线性 NSGCA 必须是最终周期性的线性 NSGCA。还将这些动力学特性的可决策性结果推广到任意限制高维线性和群 CA 的局部扰动。