This paper considers properties of a Markov chain on the natural numbers which models a binary adding machine in which there a non-zero probability of failure each time a register attempts to increment the succeeding register and resets. This chain has a family of natural quotient Markov chains, and extends naturally to a chain on the 2-adic integers. The transition operators of these chains have a self-similar structure, and have a spectrum which is, variously, the Julia set or filled Julia set of a quadratic map of the complex plane.

中文翻译：

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随机加法机和复杂动力学

本文考虑了自然数上的马尔可夫链的特性，该链对二进制加法机进行建模，其中每次寄存器尝试递增后继寄存器并重置时，故障概率都为非零。该链具有自然商马尔可夫链族，并自然地扩展到 2-adic 整数上的链。这些链的转换算子具有自相似结构，并且具有不同的谱，即复平面二次映射的朱莉娅集或填充朱莉娅集。