Abstract
In this extended abstract, we present high-level overviews of tile-based self-assembling systems capable of producing complex, infinite, aperiodic structures known as discrete self-similar fractals. Fractals have a variety of interesting mathematical and structural properties, and by utilizing the bottom-up growth paradigm of self-assembly to create them we not only learn important techniques for building such complex structures, we also gain insight into how similar structural complexity arises in natural self-assembling systems. Our results fundamentally leverage hierarchical assembly processes, and use as our building blocks square “tile” components which are capable of activating and deactivating their binding “glues” a constant number of times each, based only on local interactions. We provide the first constructions capable of building arbitrary discrete self-similar fractals at scale factor 1, and many at temperature 1 (i.e. “non-cooperatively”), including the Sierpinski triangle.
Matthew J. Patitz—This author’s research was supported in part by National Science Foundation Grant CCF-1422152.
Trent A. Rogers—This author’s research was supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-1450079, and National Science Foundation Grant CCF-1422152.
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Notes
- 1.
In this paper we refer only to “strict” self-assembly, wherein a shape is made by placing tiles only within the domain of the shape, as opposed to “weak” self-assembly where a pattern representing the shape can be formed embedded within a framework of additional tiles.
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Hendricks, J., Olsen, M., Patitz, M.J., Rogers, T.A., Thomas, H. (2016). Hierarchical Self-Assembly of Fractals with Signal-Passing Tiles. In: Rondelez, Y., Woods, D. (eds) DNA Computing and Molecular Programming. DNA 2016. Lecture Notes in Computer Science(), vol 9818. Springer, Cham. https://doi.org/10.1007/978-3-319-43994-5_6
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