A strongly universal cellular automaton on the heptagrid with seven states

In this paper, we prove that there is a strongly universal cellular automaton on the heptagrid with seven states which is rotation invariant. This improves a previous paper of the author where the automaton required ten states.Comment: 43 pages, 44 figure

A strongly universal cellular automaton in the dodecagrid with five states

In this paper, we prove that there is a strongly universal cellular automaton in the dodecagrid, the tessellation {5,3,4} of the hyperbolic 3D-space, with five states which is rotation invariant. This improves a previous paper of the author where the automaton required ten states.Comment: 49p, 22 figure