Pictures worth a thousand tiles, a geometrical programming language for self-assembly

Abstract : We present a novel way to design self-assembling systems using a notion of signal (or ray) akin to what is used in analyzing the behavior of cellular automata. This allows purely geometrical constructions, with a smaller specification and easier analysis. We show how to design a system of signals for a given set of shapes, and how to transform these signals into a set of tiles which self-assemble into the desired shapes. We show how to use this technique on three examples : squares (with optimal assembly time and a small number of tiles), general polygons, and a quasi periodic pattern : Robinson tiling.
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Theoretical Computer Science, Elsevier, 2009, 410 (16), pp.1495-1515. 〈10.1016/j.tcs.2008.12.011〉
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Florent Becker. Pictures worth a thousand tiles, a geometrical programming language for self-assembly. Theoretical Computer Science, Elsevier, 2009, 410 (16), pp.1495-1515. 〈10.1016/j.tcs.2008.12.011〉. 〈ensl-00248419v3〉

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