Generalized Langton's Ant: Dynamical Behavior and Complexity
نویسندگان
چکیده
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.
منابع مشابه
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 classifica...
متن کاملDynamical behavior and complexity of Langton's ant
O ne of the first models of artificial life, proposed back in the 1980s by Christopher Langton, founder of the field, was the virtual ant [1,2]. This simple cellular automaton is defined on the square grid in the following way: each square (“cell”) of the grid can be in one of two states, white or black, and the ant is represented by a short arrow that stands on one cell and points to the north...
متن کاملFrom Complexity to Random Behaviors; Generate Random Numbers by Confusion in Cellular Automata State’s
Cellular Automata(CA) with evolutionary and complex behaviors are used in several applications such as generating random numbers and cryptography. Because of the intrinsic self-organizing property, pure CA cannot produce a long sequence of random numbers. For increasing the sequence of produced numbers, nonuniform CA, controllable/programmable CA, stimulating factors or combination of several a...
متن کاملComplexity of Langton's ant
The virtual ant introduced by Langton [Physica D 22 (1986) 120] has an interesting behavior, which has been studied in several contexts. Here we give a construction to calculate any boolean circuit with the trajectory of a single ant. This proves the P-hardness of the system and implies, through the simulation of one-dimensional cellular automata and Turing machines, the universality of the ant...
متن کاملKolmogorov complexity and cellular automata classification
We present a new approach to cellular automata (CA for short) classification based on algorithmic complexity. We construct a parameter κ which is based only on the transition table of CA and measures the “randomness” of evolutions; κ is better, in a certain sense, than any other parameter recursively definable on CA tables. We investigate the relations between the classical topological approach...
متن کامل