Intrinsic universality in automata networks II: Glueing and gadgets

An automata network (AN) is a finite graph where each node holds a state from a finite alphabet and is equipped with a local map defining the evolution of the state of the node depending on its neighbors. This paper is the second of a series about intrinsic universality, i.e. the ability for a family of AN to simulate arbitrary AN. We develop a proof technique to establish intrinsic simulation and universality results which is suitable to deal with families of symmetric networks where connections are non-oriented. It is based on an operation of glueing of networks, which allows to produce complex orbits in large networks from compatible pseudo-orbits in small networks. As an illustration, we give a short proof that the family of networks where each node obeys the rule of the ‘game of life’ cellular automaton is strongly universal. In the third paper of the series, we heavily rely on this proof technique to show intrinsic universality results of various families with particular update schedules.