Smart Tile Self-Assembly and Replication

We propose the concept of self-assembly of smart tiles, i.e., tiles which possess a local computational device in addition to having edge glues that can be activated or deactivated by signals. We demonstrate the potential of self-assembly with smart tiles to efficiently perform robotic tasks such as the replication of convex shapes. The smart tile assembly system we construct does not make any assumption on the glues and signals of the interior tiles of the input supertile, and uses a scaffold to assemble a replica underneath it. The tile local computational device can range from its being absent to being a counter, a simple look-up table, a finite state machine, all the way to being a Turing machine. Thus, this model offers a general framework to discuss and compare various tile self-assembly systems.