On the Equivalence of Cellular Automata and the Tile Assembly Model

In this paper, we explore relationships between two models of systems which are governed by only the local interactions of large collections of simple components: cellular automata (CA) and the abstract Tile Assembly Model (aTAM). While sharing several similarities, the models have fundamental differences, most notably the dynamic nature of CA (in which every cell location is allowed to change state an infinite number of times) versus the static nature of the aTAM (in which tiles are static components that can never change or be removed once they attach to a growing assembly). We work with 2-dimensional systems in both models, and for our results we first define what it means for CA systems to simulate aTAM systems, and then for aTAM systems to simulate CA systems. We use notions of simulate which are similar to those used in the study of intrinsic universality since they are in some sense strict, but also intuitively natural notions of simulation. We then demonstrate a particular nondeterministic CA which can be configured so that it can simulate any arbitrary aTAM system, and finally an aTAM tile set which can be configured so that it can be used to simulate any arbitrary nondeterministic CA system which begins with a finite initial configuration.Comment: In Proceedings MCU 2013, arXiv:1309.104

Self-Replicating Machines in Continuous Space with Virtual Physics

JohnnyVon is an implementation of self-replicating machines in continuous two-dimensional space. Two types of particles drift about in a virtual liquid. The particles are automata with discrete internal states but continuous external relationships. Their internal states are governed by finite state machines but their external relationships are governed by a simulated physics that includes Brownian motion, viscosity, and spring-like attractive and repulsive forces. The particles can be assembled into patterns that can encode arbitrary strings of bits. We demonstrate that, if an arbitrary "seed" pattern is put in a "soup" of separate individual particles, the pattern will replicate by assembling the individual particles into copies of itself. We also show that, given sufficient time, a soup of separate individual particles will eventually spontaneously form self-replicating patterns. We discuss the implications of JohnnyVon for research in nanotechnology, theoretical biology, and artificial life