Sensors and controls in the analysis of distributed systems
Sensors and controls in the analysis of distributed systems
Models of massive parallelism: analysis of cellular automata and neural networks
Models of massive parallelism: analysis of cellular automata and neural networks
Modeling nature: cellular automata simulations with Mathematica
Modeling nature: cellular automata simulations with Mathematica
Regular Article: Cellular Automaton Growth on Z2: Theorems, Examples, and Problems
Advances in Applied Mathematics
Feedback spreading controls for semilinear parabolic systems
Journal of Computational and Applied Mathematics - control of partial differential equations
Feedback Spreading Control under Speed Constraints
SIAM Journal on Control and Optimization
Theory of Self-Reproducing Automata
Theory of Self-Reproducing Automata
A mathematical method for control problems on cellular automata models
International Journal of Systems Science
Spreadable probabilistic cellular automata models: an application in epidemiology
ACRI'06 Proceedings of the 7th international conference on Cellular Automata for Research and Industry
Cellular automata modelling and spreadability
Mathematical and Computer Modelling: An International Journal
Mathematical and Computer Modelling: An International Journal
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The spreadable phenomena which describes the expansion in time of a given spatial property has been studied using models based on partial differential equations. These spreadable dynamics are generally non-linear and then difficult to simulate particularly in two dimensions. In this article, we propose cellular automata (CA) models as an alternative modelling tool that can easily simulate spreadable systems. CA are capable of describing complex systems based on simple evolution rules, which provide numerical schemes directly implemented on computers without approximation or rounding errors. We design local CA dynamics which allow us to maintain a spatial property on non-decreasing subdomains. Several numerical results are performed to illustrate spreadable phenomena. The simulation results corroborate the general shape theory that exhibits the convergence to a specific domain independently on initial conditions.