x (coprime)

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Biham-Middleton-Levine Traffic Model

This is a cellular automaton which exhibits phase transitions and self-organisation. It consists of some cars that can only move downwards (blue), and others that can only move rightwards (red).

The two types of cars take turns to move. Each type of car can only move forwards if there is a space in front of it, otherwise it stays put. The cars are placed in random starting positions with a given density ρ. They are placed on a toroidal 2D lattice, such that the right edge is connected to the left and the bottom is connected to the top.

Phase Transitions

The BML model has two primary phases: a free-flowing phase, where a low density of cars will self-organise and produce a smooth flow of traffic; and a jammed phase where no cars can move.

There are also intermediate phases that combine jammed and free-flowing phases, in either a periodic or disordered manner.

Lattice Dimensions

The behaviour of the model depends on the exact dimensions of the lattice as well as the initial density of the cars.

Dimensions that are coprime tend to produce periodic intermediate phases near the transition density, and disordered phases for non-coprime dimensions. However, this is not always the case e.g. periodic phases have also been found for square lattices such as 128x128 at ρ=0.36.

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