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Journal Articles Theoretical Computer Science Year : 2009

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

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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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Dates and versions

ensl-00248419 , version 1 (08-02-2008)
ensl-00248419 , version 2 (14-02-2008)
ensl-00248419 , version 3 (14-02-2008)

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Florent Becker. Pictures worth a thousand tiles, a geometrical programming language for self-assembly. Theoretical Computer Science, 2009, 410 (16), pp.1495-1515. ⟨10.1016/j.tcs.2008.12.011⟩. ⟨ensl-00248419v3⟩
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