This paper presents a mathematical model for a mechanical computer called the Turing Tumble. We show that our model called Turing Tumble Model (TTM) is computationally universal under the assumptions that a configuration of TTM is sufficiently large and that local interactions between elements can be transferred without limitations. The Turing Tumble has a strict constraint, based on gravity, since signals can only move from top to bottom. We introduce a uniform scheme that takes into account this restriction in directionality to construct universal machines in the TTM based on directed acyclic graphs. This model may be useful for implementing computers that exploit mechanical interactions in nature, especially those on micrometer-scales.

本文介绍了一种称为Turing Tumble的机械计算机的数学模型。我们表明，在TTM的配置足够大且元素之间的局部交互可以不受限制地进行传输的假设下，称为图灵翻滚模型（TTM）的模型在计算上是通用的。Turing Tumble基于重力具有严格的约束，因为信号只能从顶部移动到底部。我们介绍了一种统一的方案，该方案考虑了方向性的这种限制，以便根据有向无环图在TTM中构造通用机器。该模型对于实施利用自然界中的机械相互作用（尤其是微米级的机械相互作用）的计算机可能有用。