Difference between revisions of "Hierarchical Self-Assembly of Fractals with Signal-Passing Tiles"
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|date=2016/09/04 | |date=2016/09/04 | ||
|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. | |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. | ||
| − | |authors=Jacob Hendricks, Meagan Olsen, Matthew J. Patitz, Trent A. Rogers, | + | |authors=Jacob Hendricks, Meagan Olsen, Matthew J. Patitz, Trent A. Rogers, Hadley Thomas |
|file=http://arxiv.org/pdf/1606.01856v1 | |file=http://arxiv.org/pdf/1606.01856v1 | ||
}} | }} | ||
Revision as of 13:03, 21 June 2016
Published on: 2016/09/04
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.
Authors
Jacob Hendricks, Meagan Olsen, Matthew J. Patitz, Trent A. Rogers, Hadley Thomas
