2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/135697Some linear dynamical systems over finite fields are studied and the self-similar character of their development is proved. Connections with aperiodic tilings, Delanoy numbers and other topics are also proved. The prime fields F_p have a canonical presentation as sets of self-similar carpets. The multiplicative inverse corresponds to mirroring.14 pages, some latex figures in text (no separate files) These results have been presented at CiE 2007, Siena, ItalyNumber TheoryCombinatorics11A07, 28A80text