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arXiv · 1503.01244

Replication of arbitrary hole-free shapes via self-assembly with signal-passing tiles

Andrew Alseth·Jacob Hendricks·Matthew J. Patitz·Trent A. Rogers
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Abstract

In this paper, we investigate the abilities of systems of self-assembling tiles which can each pass a constant number of signals to their immediate neighbors to create replicas of input shapes. Namely, we work within the Signal-passing Tile Assembly Model (STAM), and we provide a universal STAM tile set which is capable of creating unbounded numbers of assemblies of shapes identical to those of input assemblies. The shapes of the input assemblies can be arbitrary 2-dimensional hole-free shapes. This improves previous shape replication results in self-assembly that required models in which multiple assembly stages and/or bins were required, and the shapes which could be replicated were more constrained, as well as a previous version of this result that required input shapes to be represented at scale factor 2.

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Andrew Alseth, Jacob Hendricks, Matthew J. Patitz, Trent A. Rogers. 2015-03-04. Replication of arbitrary hole-free shapes via self-assembly with signal-passing tiles. https://arxiv.org/abs/1503.01244

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