Self-healing Tile Sets

Molecular self-assembly appears to be a promising route to bottom-up fabrication of complex objects. Two major obstacles are how to create structures with more interesting organization than periodic or finite arrays, and how to reduce the fraction of side products and erroneous assemblies. Algorithmic self-assembly provides a theoretical model for investigating these questions: the growth of arbitrarily complex objects can be programmed into a set of Wang tiles, and their robustness to a variety of possible errors can be studied. The ability to program the tiles presents an alternative to directly physical or chemical means for reducing error rates, since redundant information can be stored so that errors can be detected, corrected, and/or prevented during the self-assembly process. Here we study the ability of algorithmic self-assembly to heal damage to a self-assembled object. We present block transforms that convert an original error-prone tile set into a new tile set that performs the same construction task (at a slightly larger scale) and also is able to heal damaged areas where many tiles have been removed from the assembly.