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This paper answers a long-standing open question in tile-assembly theory, namely that it is possible to strictly assemble discrete self-similar fractals (DSSFs) in the abstract Tile-Assembly Model (aTAM). We prove this in 2 separate ways, each taking
Externí odkaz:
http://arxiv.org/abs/2406.19595
Tile assembly systems in the abstract Tile Assembly Model (aTAM) are computationally universal and capable of building complex shapes, but DNA-based implementations encounter formidable error rates that stifle this theoretical potential. Slat-based s
Externí odkaz:
http://arxiv.org/abs/2405.06205
Autor:
Hader, Daniel, Patitz, Matthew J.
Algorithmic self-assembly occurs when disorganized components autonomously combine to form structures and, by their design and the dynamics of the system, are forced to follow the execution of algorithms. Motivated by applications in DNA-nanotechnolo
Externí odkaz:
http://arxiv.org/abs/2305.01877
In this paper, we investigate shape-assembling power of a tile-based model of self-assembly called the Signal-Passing Tile Assembly Model (STAM). In this model, the glues that bind tiles together can be turned on and off by the binding actions of oth
Externí odkaz:
http://arxiv.org/abs/2206.03908
In this paper we present a model containing modifications to the Signal-passing Tile Assembly Model (STAM), a tile-based self-assembly model whose tiles are capable of activating and deactivating glues based on the binding of other glues. These modif
Externí odkaz:
http://arxiv.org/abs/2105.02914
We present a series of results related to mathematical models of self-assembling tiles and the impacts that three diverse properties have on their dynamics. We expand upon a series of prior results which showed that (1) the abstract Tile Assembly Mod
Externí odkaz:
http://arxiv.org/abs/1910.03950
Autor:
Hader, Daniel, Patitz, Matthew J.
Tile-based self-assembly systems are capable of universal computation and algorithmically-directed growth. Systems capable of such behavior typically make use of "glue cooperation" in which the glues on at least $2$ sides of a tile must match and bin
Externí odkaz:
http://arxiv.org/abs/1903.05774
Publikováno v:
Natural Computing; Sep2024, Vol. 23 Issue 3, p497-530, 34p
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