Papers

The elementary cellular automaton following rule 184 can mimic particles flowing in one direction at a constant speed. Therefore, this automaton can model highway traffic qualitatively. In a recent paper, we have incorporated intersections regulated by traffic lights to this model using exclusively elementary cellular automata. In such a paper, however, we only explored a rectangular grid. We now extend our model to more complex scenarios using an hexagonal grid. This extension shows first that our model can readily incorporate multiple-way intersections and hence simulate complex scenarios. In addition, the current extension allows us to study and evaluate the behavior of two different kinds of traffic-light controller for a grid of six-way streets allowing for either two- or three-street intersections: a traffic light that tries to adapt to the amount of traffic (which results in self-organizing traffic lights) and a system of synchronized traffic lights with coordinated rigid periods (sometimes called the “green-wave” method). We observe a tradeoff between system capacity and topological complexity. The green-wave method is unable to cope with the complexity of a higher-capacity scenario, while the self-organizing method is scalable, adapting to the complexity of a scenario and exploiting its maximum capacity. Additionally, in this article, we propose a benchmark, independent of methods and models, to measure the performance of a traffic-light controller comparing it against a theoretical optimum.

We show novel techniques of analysing complex dynamics of cellular automata (CA) with chaotic behaviour. CA are well known computational substrates for studying emergent collective behaviour, complexity, randomness and interaction between order and disorder. A number of attempts have been made to classify CA functions on their spatio-temporal dynamics and to predict behavior of any given function. Examples include mechanical computation, lambda and Z-parameters, mean field theory, differential equations and number conserving features. We propose to classify CA based on their behaviour when they act in a historical mode, i.e. as CA with memory. We demonstrate that cell-state transition rules enriched with memory quickly transform a chaotic system converging to a complex global behaviour from almost any initial condition. Thus in just a few steps we can select chaotic rules without exhaustive computational experiments or recurring to additional parameters. We provide analysis of well-known chaotic functions in one-dimensional CA, and decompose dynamics of the automata using majority memory.