A pseudo-random network mobile automaton with linear growth

Based on the mobile automaton model, an algorithm is introduced that grows planar, tri-valent graphs by exhibiting a peculiar, twofold dynamics. In a first phase, graph growth appears to be pseudo-random and O(n); then it settles to a very regular behavior and O(Sqrt(n)) rate. A pseudo-random O(Sqrt(n)) mobile automaton is already known; the new automaton provides now a finite, but surprisingly long, pseudo-random, linear growth process. Applications of mobile automata to fundamental physics and quantum gravity have been recently suggested.