不动点和非周期镶嵌
Fixed Point and Aperiodic Tilings
摘要：
R.Berger在证明多米诺骨牌问题的不可判定性时首先构造了一个非周期瓦片集。事实证明，非周期瓦片集出现在许多主题，从逻辑（Entscheidungsproblem）到物理（quasicrystals）。我们提出了一个新的非周期瓦片集的构造，它是基于Kleene的不动点构造，而不是几何参数。这种构造类似于J·冯·诺依曼的自复制自动机; P. Gacs在纠错计算的上下文中也使用了类似的想法。这种构造的灵活性允许我们构造一个“鲁棒的”非周期性瓦片集，即使我们允许一些（足够稀疏的）瓦片错误，该瓦片集也不具有周期性（或接近周期性）瓦片。此属性对于任何现有的非周期性图块集都是未知的。
英文摘要：
An aperiodic tile set was first constructed by R.Berger while proving the undecidability of the domino problem. It turned out that aperiodic tile sets appear in many topics ranging from logic (the Entscheidungsproblem) to physics (quasicrystals) We present a new construction of an aperiodic tile set that is based on Kleene's fixed-point construction instead of geometric arguments. This construction is similar to J. von Neumann self-reproducing automata; similar ideas were also used by P. Gacs in the context of error-correcting computations. The flexibility of this construction allows us to construct a "robust" aperiodic tile set that does not have periodic (or close to periodic) tilings even if we allow some (sparse enough) tiling errors. This property was not known for any of the existing aperiodic tile sets.
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