Dynamics of a class of ants on a one-dimensional lattice

A one-dimensional virtual ant is an automaton evolving in the lattice Z. Each cell of Z may have white or black color. The ant, represented by an arrow in a cell, moves to a neighbor and may change the color of the current cell depending on its previous color. In this paper we characterize into classes the dynamics of 64 ant's rules, taking into account bounded or unbounded evolution as well as the periods and the steady-state behavior. We describe in a detailed way the behavior of each of the rules, determining the steady state velocity, period and transient time.