Cellular automata (CA) can be viewed as a mathematical abstraction of the physical world in which all quantities are of discrete nature. Due to its simplicity, CA turn out to a be very interesting approach to model complex systems in which a macroscopic collective behavior emerges out of the interaction of many simple elements. This school will indroduce this approach in a pedagogical way through many examples illustrating the essence of CA modeling.
The program is the following:
- Introduction: What are CA’s?: computational model, discrete dynamical system, abstraction of physical and natural systems
- Definition: Parity rule. Neighborhood, stochastic CA, non-uniform CA, asynchronous CA. Implementation: lookup table, on the fly computation. Number of possible universe
- Historical notes: from von-Neumann to Langton self-reproduction CA
- Modeling of physical system: create a fititious world where conservation laws and symmetries are preserved.
Examples: snowflakes, excitable media,…
traffic models, homostatis,…
- Understanding complex systems through CAs: life, Langton ants, Wol- fram complexity classes…
- Lattice gases: CA fluids, diffusion models, exact computation and re- versibility
- Extension: lattice Boltzmann, multi-agent: in-silico modeling at a mesoscopic level.
- Exercises: will be inserted during the presentation
Additional Information: For PhD students from the University of Milano-Bicocca the school is valid for one course credit.
The school will continue with the workshops to introduce the students to recent research results on various aspects of CA.
CA: why and what?
installing the software and implementing the parity rule. Explore some behaviors (asynchronous/synchronous).
Formal definition of a CA, neighborhoods, boundary conditions, etc
||Theory: Historical notes, von Newman & Langton CA; CA as a modeling tool: snowflakes; other examples (drosophila, greenberg-hastins, forest fire, homeostastis,…)
Greenberg-Hasting, forest fire, etc
Complex systems (game of life, Langton’s ant, parity, universal computer, Wolfram’s rules).
Discussion: parity, universal computer, intractability
CA traffic models
Lattice Gas Automata and Lattice Boltzmann models.
Bastien Chopard is full professor at the University of Geneva, and group leader in the Swiss Institute of Bioinformatics. He earned his PhD in theoretical physics from the University of Geneva in 1988. He then spent two years as a postdoc in the laboratory for computer science at MIT (Cambridge, USA), and one year in the Research Center, Juelich (Germany) before joining the computer science department at University of Geneva. His main research interests is the modeling and simulation of complex systems. He is internationally recognized for his work on Cellular Automata and Lattice Boltzmann methods. He wrote more than 200 scientific articles, presenting interdisciplinary research in various fields, such as physics, social and environmental science, bio-medical applications, numerical and optimization methods, parallel computing and multiscale modeling.
Jean-Luc Falcone is a senior research associate and lecturer at the University of Geneva. After studying biology, he obtained in 2008 an interdisciplinary PhD in biology and computer science. Since 2010, he holds the position of HPC application analyst at CADMOS (Center for the Advanced Modelling of Science). His research interests include bioinformatics, multi-science models, multi-scale systems and parallel computing.