  Self-assembly refers to the process by which small, simple components mix and
combine to form complex structures using only local interactions. Designed as a
hybrid between tile assembly models and cellular automata, the Tile Automata
(TA) model was recently introduced as a platform to help study connections
between various models of self-assembly. However, in this paper we present a
result in which we use TA to simulate arbitrary systems within the amoebot
model, a theoretical model of programmable matter in which the individual
components are relatively simple state machines that are able to sense the
states of their neighbors and to move via series of expansions and
contractions. We show that for every amoebot system, there is a TA system
capable of simulating the local information transmission built into amoebot
particles, and that the TA "macrotiles" used to simulate its particles are
capable of simulating movement (via attachment and detachment operations) while
maintaining the necessary properties of amoebot particle systems. The TA
systems are able to utilize only the local interactions of state changes and
binding and unbinding along tile edges, but are able to fully simulate the
dynamics of these programmable matter systems.

Emerging Technologies