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 Sierpinski 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 and the initial configuration has finite support. The spacetime diagram then has a property related to k-automaticity. We show that these conditions can be relaxed: the Abelian group can be a commutative monoid, the initial configuration can be k-automatic, and the spacetime diagrams still exhibit the same regularity.

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