A universal cellular automaton on the heptagrid of the hyperbolic plane with four states

In this paper, we construct a new weakly universal cellular automaton on the ternary heptagrid. This significantly improves the previous result, obtained by the same author in the same grid with six states. This time, the number of states is four. This is the best result up to date for cellular automata in the hyperbolic plane, with true planar motions.