Definition and Behavior of Langton's Ant in Three Dimensions

The "virtual ant" automaton was invented by C. Langton [1]. It has an interesting behavior that has been studied in several researches. A definition of generalized ants in three dimensions, as an extension to Langton's ant, is given here. The phenomenon of periodic motion with drift, the so-called "highway," is also observed in three dimensions but occurs in very different forms. Two classification systems of three-dimensional ants according to the period length of their highways and the resources they need before building a highway are presented.