2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65311If A=Z/2, then A^Z is a compact abelian group. A `linear cellular automaton' is a shift-commuting endomorphism F of A^Z. If P is a probability measure on A^Z, then F `asymptotically randomizes' P if F^j P converges to the Haar measure as j-->oo, for j in a subset of Cesaro density one. Via counterexamples, we show that nonzero entropy of P is neither necessary nor sufficient for asymptotic randomization.8 pagesDynamical SystemsProbability37B15 (primary), 68Q80 (secondary)text