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

Becker Florent (1)

1 LIP - Laboratoire de l'Informatique du Parallélisme

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.

Mots clés: Self-assembly; Signals; Polygons; Tilings; Robinson

Domaines: Mathématique discrète [cs.DM]

Becker Florent. Pictures worth a thousand tiles, a geometrical programming language for self-assembly. 2008. ⟨ensl-00248419v2⟩