Dynamic Simulation of 1D Cellular Automata with DNA-based Tiles

We show how one-dimensional cellular automata can be dynamically simulated by DNAbased tiles within the Active Abstract Tile Assembly Model (Active aTAM). The Active aTAM is a tile model for self assembly where tiles are able to transfer signals and change identities according to the signals received. We give a brief description of the model with the dynamics of tile attachment and signal passing and extend it to include deactivation signals and detachment of tiles. We then show that the extended model allows a simulation of cellular automata with assemblies that do not record the entire computational history but only the current updates of the states, demonstrating the idea of reusable space in selfassembly. The simulation is such that at a given location the sequence of tiles that attach and detach corresponds precisely to the sequence of states the synchronous cellular automaton generates at that location.