Strategies and Rubrics for Teaching Chaos and Complex Systems Theories as Elaborating, Self-Organizing, and Fractionating Evolutionary Systems Fichter, Lynn S., Pyle, E.J., and Whitmeyer, S.J., 2010, Journal of Geoscience Education (in press)

Cellular Automata

Cellular Automata and Self Organization Cellular Automata (CA) are simply grids of cells, where the individual cells change states according to a set of rules. The CA may be one dimensional, or linear, like a string of cells in a row (below), or two dimensional, like a checkerboard Optimal Local Rule Set Survival Rules – 2/3 a live cell survives to the next generation if at least 2 but no more than three of the surrounding 8 cells are alive. Less than 2 and it dies of loneliness; more than 3 and it dies of over crowding.- Birth Rules – 3/3 a dead cells comes alive the next generation if 3, any 3, of the surrounding 8 cells are also alive. Local Rules/Global Behavior ? Now, as cells are added, which will come alive, which survive?

Cellular Automata and Self Organization

Classifying Cellular Automata Rules Stephen Wolfram Class One - Fixed or Static: Rules that produce dull universes, such as all dead cells or all living cells; e.g. ice. Class Two - Periodic or Oscillatory: Rules that produce stable, repetitive configurations. Class Three - Chaotic: Rules that produce chaotic patterns; e.g. molecules in a gas. Class Four - Complexity: Rules that produce complex, locally organized patterns; e.g. behave like a flowing liquid..

Classifying Cellular Automata Rules Chris Langton

Power-Law Relationships in Cellular Automata Run a random array until it stops, add a live cell at random, run again until it stops. Avalanche size is the number of generations from initiation until it stops. Most avalanches last only one or a few generations; others may last hundreds of generations. Plotted up the avalanches follow a power-law meaning Cellular Automata (with optimum local rules) are Self Organized Critical systems.

Evolution of Ripples A cellular automata model Mechanics of Wind Ripple Stratigraphy Author(s): Spencer B. Forrest and Peter K. Haff Source: Science, New Series, Vol. 255, No (Mar. 6, 1992), pp Published by: American Association for the Advancement of Science

Cellular Automata Examples