三角形和六边形保数元胞自动机的模拟
Simulations between triangular and hexagonal number-conserving cellular automata
摘要：
数守恒元胞自动机是一种状态为整数的元胞自动机，其转换函数在整个演化过程中保持所有元胞的和不变。它可以被看作是质量或能量守恒定律的一种模型化。在本文中，我们首先提出了一个必要条件，三角形和六角形细胞自动机是数量守恒。局部转移函数表示为任意两个函数之和，可以看作是数的“流”。充分性是通过关于保数元胞自动机的一般结果得到的。然后，利用前面的流函数，我们可以构造出六角元胞自动机和三角元胞自动机之间有效的保数模拟。
英文摘要：
A number-conserving cellular automaton is a cellular automaton whose states are integers and whose transition function keeps the sum of all cells constant throughout its evolution. It can be seen as a kind of modelization of the physical conservation laws of mass or energy. In this paper, we first propose a necessary condition for triangular and hexagonal cellular automata to be number-conserving. The local transition function is expressed by the sum of arity two functions which can be regarded as 'flows' of numbers. The sufficiency is obtained through general results on number-conserving cellular automata. Then, using the previous flow functions, we can construct effective number-conserving simulations between hexagonal cellular automata and triangular cellular automata.
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