Alan Jolly, University of Central Florida, Modeling and Simulation


Cellular Automata and the Study of Complex Systems

Abstract: Cellular Automata (CA) are simple representations of dynamical systems which typically have more than two interacting nonlinear parts that are discrete in both time and space. They are useful for the study of general pattern formation and the emergent behaviors of complex systems. Formal CA models have 5 general characteristics: i) A discrete lattice of cells, ii) homogeneity (all cells are equivalent), iii) cells take on a finite number of discrete states, iv) cells interact only with their local neighborhood, and v) cell updates are performed at discrete time intervals according to transitions rules that account for the state of cells within a neighborhood.

There are many variants of CA that relax characteristics of the formal CA. Three which are used in the field agent based modeling are coupled-map lattices, probabilistic CA, and mobile CA. My research interests include extending a model of pedestrian crowd dynamics that uses all three of these variants. Pedestrian movement between cells is based on stochastic transition rules. Pedestrians move across the lattice but are unable to occupy the same cell. Pedestrian ÔintelligenceÕ is modeled through the use of static and dynamic floor fields.

CA models may also be used as discrete representations of partial differential equations. Interesting current works have directly linked CA to soliton solutions for nonlinear waves and a methodology for constructing partial-differential equations directly from CA transition rules has been proposed. PDEÕs have been constructed from WolframÕs elementary cellular automata. This may be a first step towards resolving a limiting factor of CA Ð a lack of methods for through mathematical analysis.

Advisor: David Kaup (UCF)