This paper describes a sequence of natural numbers that grows faster than any Turing computable function. This sequence is generated from a version of the tiling problem, called a coloring system. In our proof that generates the sequence, we use the notions of a chain and an unbounded sequence property, which resemble the methods of point set topology. From this sequence, we define a Turing incomputable coloring function.

翻译：本文描述了一个增长速度超过任何图灵可计算函数的自然数序列。该序列源于一种名为着色系统的拼贴问题变体。在生成该序列的证明过程中，我们使用了链和无界序列性质等概念，这些概念类似于点集拓扑学的方法。基于该序列，我们定义了一个图灵不可计算的着色函数。