We investigate a simple a discrete time random process based on the construction of Platonic solids. As is surprisingly often the case with apparently simple processes, we find some intriguing results, in this case requiring a careful consideration of how the probability distributions describing this process behave. The investigation proceeds by a fruitful combination of geometry, probability and elementary real analysis. We conclude with a consideration of the limiting behaviour of the probability distributions describing the size of the solid as the number of steps grows.

中文翻译：

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随机进化的柏拉图式固体：零玩家游戏

我们研究了基于柏拉图固体的简单离散时间随机过程。令人惊讶的是，看起来很简单的过程经常出现这种情况，我们发现了一些有趣的结果，在这种情况下，需要仔细考虑描述此过程的概率分布的行为方式。通过几何，概率和基本实数分析的卓有成效的结合，进行了调查。我们以考虑概率分布的极限行为作为结束，该概率分布描述了随着步数的增长而形成的实体的大小。