We introduce a hierarchical self assembly algorithm that produces the quasiperiodic patterns found in the Robinson tilings and suggest a practical implementation of this algorithm using DNA origami tiles. We modify the abstract Tile Assembly Model (aTAM), to include active signaling and glue activation in response to signals to coordinate the hierarchical assembly of Robinson patterns of arbitrary size from a small set of tiles according to the tile substitution algorithm that generates them. Enabling coordinated hierarchical assembly in the aTAM makes possible the efficient encoding of the recursive process of tile substitution.

中文翻译：

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来自 Robinson 瓷砖的分层自组装模式：增强型瓷砖组装模型中的 DNA 瓷砖设计。

我们引入了一种分层自组装算法，该算法产生在 Robinson 拼贴中发现的准周期模式，并建议使用 DNA 折纸拼贴实际实现该算法。我们修改了抽象的瓦片组装模型 (aTAM)，包括响应信号的主动信号和胶水激活，以根据生成它们的瓦片替换算法从一小组瓦片中协调任意大小的罗宾逊图案的分层组装。在 aTAM 中启用协调的分层组装使得对瓦片替换递归过程的有效编码成为可能。