Generalized Langton's Ant: Dynamical Behavior and Complexity

Langton’s ant is a simple discrete dynamical system, with a surprisingly complex behavior. We study its extension to general planar graphs. First we give some relations between characteristics of finite graphs and the dynamics of the ant on them. Then we consider the infinite bi-regular graphs of degrees 3 and 4, where we prove the universality of the system, and in the particular cases of the square and the hexagonal grids, we associate a P-hard problem to the dynamics. Finally, we show strong spatial restrictions on the trajectory of the ant in infinite bi-regular graphs with degrees strictly greater than 4, which contrasts with the high unpredictability on the graphs of lower degrees.

• Type: Conference
• Year: 2001
• Where: STACS
• Authors: Anahí Gajardo, Eric Goles Ch., Andrés Moreira
• Keywords: Discrete Dynamical System, General Planar Graphs, Infinite Bi-regular Graphs, STACS 2001, Theoretical Computer Science