Grammatical Self Assembly for Planar Tiles

Abstract

We introduce a formal grammatical process for planar self-assembling systems with conformal switching which instantiates the geometry of the tiles. This extends prior work which gave a grammatical structure that models only the topology of the assembly. The addition of geometric data leads to the problem of determining which sets of grammatical rules preserve the planar constraint. We illustrate global obstructions while generating examples of rule sets which intrinsically force the preservation of planar geometry.