  It is well-known that the spacetime diagrams of some cellular automata have a
fractal structure: for instance Pascal's triangle modulo 2 generates a
Sierpi\'nski triangle. It has been shown that such patterns can occur when the
alphabet is endowed with the structure of an Abelian group, provided the
cellular automaton is a morphism with respect to this structure. The spacetime
diagram then has a property related to $k$-automaticity. We show that this
condition can be relaxed from an Abelian group to a commutative monoid, and
that in this case the spacetime diagrams still exhibit the same regularity.
