We present a simple approach for finding all number-conserving two-dimensional cellular automata with the von Neumann neighborhood. We demonstrate the efficiency of this approach by enumerating and describing four special cases: totalistic, outer-totalistic, binary and three-state cellular automata. The last result was not published before. We then proceed to find all reversible two-dimensional number-conserving cellular automata with three states with the von Neumann neighborhood and show there are only trivial ones.

中文翻译：

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三态二维保数元胞自动机的有效枚举

我们提出一种简单的方法来查找所有与冯·诺依曼邻域保持二维数的自动机。我们通过枚举和描述四个特殊情况来证明这种方法的效率：总量，外总，二进制和三态细胞自动机。最后结果未发布。然后，我们继续寻找具有von Neumann邻域的三个状态的所有可逆的二维守恒细胞自动机，并证明其中只有少量。