Abstract
A complex system is a set of mutually interacting elements for which it is possible to construct a mathematical model. This article focuses on the cellular automata theory and the graph theory in order to compare various types of cellular automata and to analyse applications of graph structures together with cellular automata. It proposes a graph cellular automaton with a variable configuration of cells and relation-based neighbourhoods (r–GCA). The developed mechanism enables modelling of phenomena found in complex systems (e.g., transport networks, urban logistics, social networks) taking into account the interaction between the existing objects. As an implementation example, modelling of moving vehicles has been made and r–GCA was compared to the other cellular automata models simulating the road traffic and used in the computer simulation process.
Highlights
Cellular automata (CA), described by cell structure, rules and possible states, are mathematical models functioning as a modelling environment for discrete systems
The stochastic nature of road traffic and its complexity allows for the application of a graph cellular automaton with relation-based neighbourhoods
This article presents a novel approach to the understanding of graph cellular automata
Summary
Cellular automata (CA), described by cell structure, rules and possible states, are mathematical models functioning as a modelling environment for discrete systems. CA development led to the creation of many types and implementations of both homogeneous and nonhomogeneous, structurally dynamic [2,3], asynchronous automata designed to explore the processes taking place in the real world [4,5], and graph automata, nonhomogeneous on the grounds of the different cardinality of the neighbourhood of individual cells [6,7,8]. A structurally dynamic relative neighbourhood cellular automaton is described. In order to define it, after a short presentation of the CA definition, a reconfigurable graph acting as a tool for describing the modelled objects (system elements) and their relative neighbourhoods will be discussed. A graph cellular automaton (r–GCA) will be presented, along with the possibilities of its implementation in defined systems, as sets of the same type related objects.
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