In this article, I present two versions of a cellular automaton (CA) that evolve according to a set of rules derived from a well-known combinatorial structure: Pascal’s Triangle. These CAs produce point sampling commonly observed in high-quality digital dithering and halftoning techniques. The first version is a probabilistic cellular automaton (PCA), which samples discrete values from Pascal’s Triangle as a probability distribution. The second version is deterministic, where tone-dependent lattice paths are selected from Pascal’s Triangle by analyzing the local points distribution in the halftone pattern. This deterministic version also offers significant computational gains over its probabilistic counterpart.