Elementary Cellular Automata as Dynamical Systems

First Prize, DSWeb Tutorials Contest

By Sam Reid
Elementary Cellular Automata as Dynamical Systems
This Interactive Tutorial introduces Elementary Cellular Automata as Dynamical Systems. Cellular Automata are Dynamical Systems which are temporally and spatially discrete, and the update mechanism is spatially local. 

Elementary Cellular Automata are 1-Dimensional, 2-Neighbor, 2-State Cellular Automata. These restrictions, while making the system easier to visualize, do not hinder the system's emergent behavior. On the contrary, Elementary Cellular Automata exhibit emergent behavior including fractals, complexity, chaos and embedded particles. In fact, it was recently proved that any computable function can be computed by an infinite Elementary Cellular Automaton. 

In this tutorial, we study these Cellular Automata and depict their complex emergent behavior. We hope an exploration of this powerful dynamical system will confer insight into many forms of dynamical systems. 

The Interactive Tutorial is parceled into three main sections: 1. Introduction The basic ideas of a cellular automata. 2. Behavior Types The four main classes of behavior. 3. Emergence Fractals, sensitivity to initial conditions, particles, the 'Edge of Chaos', dynamical parameters. 4. The Explorer A main application for exploring cellular automata. 

In the Interactive Tutorial, participants set up and run experiments and solve puzzles designed to highlight and portray properties of this Dynamical System.
Author Institutional Affiliation
Sam Reid
Department of Computer Science
University of Colorado at Boulder
Author Email
Tutorial LevelBasic Tutorial
Contest EntryYes

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