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Concept
Rule 184
Summary
Rule 184 is a one-dimensional binary cellular automaton rule, notable for solving the majority problem as well as for its ability to simultaneously describe several, seemingly quite different, particle systems:
Rule 184 can be used as a simple model for traffic flow in a single lane of a highway, and forms the basis for many cellular automaton models of traffic flow with greater sophistication. In this model, particles (representing vehicles) move in a single direction, stopping and starting depending on the cars in front of them. The number of particles remains unchanged throughout the simulation. Because of this application, Rule 184 is sometimes called the "traffic rule".
Rule 184 also models a form of deposition of particles onto an irregular surface, in which each local minimum of the surface is filled with a particle in each step. At each step of the simulation, the number of particles increases. Once placed, a particle never moves.
Rule 184 can be understood in terms of ballistic annihilation, a system of particles moving both leftwards and rightwards through a one-dimensional medium. When two such particles collide, they annihilate each other, so that at each step the number of particles remains unchanged or decreases.
The apparent contradiction between these descriptions is resolved by different ways of associating features of the automaton's state with particles.
The name of Rule 184 is a Wolfram code that defines the evolution of its states. The earliest research on Rule 184 is by and . In particular, Krug and Spohn already describe all three types of particle system modeled by Rule 184.
A state of the Rule 184 automaton consists of a one-dimensional array of cells, each containing a binary value (0 or 1). In each step of its evolution, the Rule 184 automaton applies the following rule to each of the cells in the array, simultaneously for all cells, to determine the new state of the cell:
An entry in this table defines the new state of each cell as a function of the previous state and the previous values of the neighboring cells on either side.
Official source
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