How fast does Langton’s ant move?
نویسنده
چکیده
The automaton known as ‘Langton’s ant’ exhibits a dynamical transition from a disordered phase to an ordered phase where the particle dynamics (the ant) produces a regular periodic pattern (called ‘highway’). Despite the simplicity of its basic algorithm, Langton’s ant has remained a puzzle in terms of analytical description. Here I show that the highway dynamics obeys a discrete equation where from the speed of the ant (c = √ 2/52) follows exactly.
منابع مشابه
From 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 کاملGenerating pseudo-random numbers by combining two systems with complex behaviors
Cellular automata (CA) due to its complex behavior has several applications such as generating random numbers and cryptography. Because of the intrinsic self-organized property, a pure CA cannot produce a long sequence of random numbers. Non-uniform, controllable/programmable CA or a combination of several automata can be used to increase the length of a produced sequence of random numbers. In ...
متن کاملDefinition 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 کاملNontrivial Turmites are Turing-universal
A Turmit is a Turing machine that works over a two-dimensional grid, that is, an agent that moves, reads and writes symbols over the cells of the grid. Its state is an arrow and, depending on the symbol that it reads, it turns to the left or to the right, switching the symbol at the same time. Several symbols are admitted, and the rule is specified by the turning sense that the machine has over...
متن کاملGeneralized 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 ...
متن کامل