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Self-assembly of Shapes at Constant Scale Using Repulsive Forces

机译:使用排斥力以恒定比例自组装形状

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The algorithmic self-assembly of shapes has been considered in several models of self-assembly. For the problem of shape construction, we consider an extended version of the Two-Handed Tile Assembly Model (2HAM), which contains positive (attractive) and negative (repulsive) interactions. As a result, portions of an assembly can become unstable and detach. In this model, we utilize fuel-efficient computation to perform Turing machine simulations for the construction of the shape. In this paper, we show how an arbitrary shape can be constructed using an asymptotically optimal number of distinct tile types (based on the shape's Kolmogorov complexity). We achieve this at O(1) scale factor in this straightforward model, whereas all previous results with sublin-ear scale factors utilize powerful self-assembly models containing features such as staging, tile deletion, chemical reaction networks, and tile acti-vation/deactivation. Furthermore, the computation and construction in our result only creates constant-size garbage assemblies as a byproduct of assembling the shape.
机译:在几种自组装模型中已经考虑了形状的算法自组装。对于形状构造问题,我们考虑了双手砖瓦装配模型(2HAM)的扩展版本,该模型包含正(有吸引力)和负(排斥)相互作用。结果,组件的某些部分可能变得不稳定和分离。在此模型中,我们利用节油计算来对形状的构造进行图灵机仿真。在本文中,我们展示了如何使用渐近最优数量的不同图块类型(基于形状的Kolmogorov复杂度)来构造任意形状。我们在这个简单的模型中以O(1)比例因子实现了这一目标,而以前所有具有亚耳形比例因子的结果都利用了强大的自组装模型,其中包含分期,贴图删除,化学反应网络和贴图激活/停用。此外,我们结果中的计算和构造只会创建大小固定的垃圾程序集,作为组装形状的副产品。

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