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- W2883341401 abstract "In this paper, we prove that in the abstract Tile Assembly Model (aTAM), an accretion-based model which only allows for a single tile to attach to a growing assembly at each step, there are no tile assembly systems capable of self-assembling the discrete self-similar fractals known as the “H” and “U” fractals. We then show that in a related model which allows for hierarchical self-assembly, the 2-Handed Assembly Model (2HAM), there does exist a tile assembly systems which self-assembles the “U” fractal and conjecture that the same holds for the “H” fractal. This is the first example of discrete self similar fractals which self-assemble in the 2HAM but not in the aTAM, providing a direct comparison of the models and greater understanding of the power of hierarchical assembly." @default.
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- W2883341401 date "2018-01-01" @default.
- W2883341401 modified "2023-10-17" @default.
- W2883341401 title "Hierarchical Growth Is Necessary and (Sometimes) Sufficient to Self-assemble Discrete Self-similar Fractals" @default.
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- W2883341401 doi "https://doi.org/10.1007/978-3-030-00030-1_6" @default.
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