Robust periodic solutions and evolution from seeds in one-dimensional edge cellular automata

We study one-dimensional cellular automata (CA) with values 0 and 1. We assume that such CA are started from semi-infinite configurations (those that have 0’s to the left of some site), and we focus on the identification of robust periodic solutions (RPS), which, when observed from the left edge of the light cone, advance into any environment with positive velocity. We then utilize RPS and related concepts to analyze CA dynamics from seeds, i.e., initial configurations with finitely many 1’s.