离散自相似分形的自组装
Self-Assembly of Discrete Self-Similar Fractals
摘要：
在本文中，我们搜索{ \it绝对}的瓷砖组装模型（TAM）的限制，以及技术，以解决这些限制。具体来说，我们调查的自组装的分形形状的TAM。我们证明，没有自相似分形完全弱自组装在温度1，某些类型的自相似分形不严格自组装在任何温度。此外，我们扩展的纤维结构从Lathrop等。（2007）表明，任何属于特定类别的“漂亮”自相似分形的自相似分形都有一个严格自组装在TAM中的纤维版本。
英文摘要：
In this paper, we search for {\it absolute} limitations of the Tile Assembly Model (TAM), along with techniques to work around such limitations. Specifically, we investigate the self-assembly of fractal shapes in the TAM. We prove that no self-similar fractal fully weakly self-assembles at temperature 1, and that certain kinds of self-similar fractals do not strictly self-assemble at any temperature. Additionally, we extend the fiber construction from Lathrop et. al. (2007) to show that any self-similar fractal belonging to a particular class of "nice" self-similar fractals has a fibered version that strictly self-assembles in the TAM.
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