A weakly universal cellular automaton on the pentagrid with two states

In this paper, we prove that there is a weakly universal cellular automaton on the pentagrid with two states. This paper improves in some sense a previous result with three states. Both results make use of a la Moore neighbourhood. However, the result with three states is rotation invariant while the result of the present paper is not. In both cases, at each step of the computation, the set of non quiescent states has always infinitely many cycles.