  In this paper, we construct a family of weakly universal rotation invariant
cellular automaton for all grids $\{p,3\}$ of the hyperbolic plane for $p\geq
13$. The scheme is general for $p\geq 17$ and for $13\leq p<17$, we give such a
cellular automaton for $p=13$, which is enough. Also, an important property of
this family is that the set of cells of the cellular automaton which are
subject to changes is actually a planar set. The problem for $p<13$ for a truly
planar construction is still open. The best result, for $p=7$, is four states
and was obtained by the same author.
