Self-similar carpets over finite fields

Abstract

Some 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, Italy