Competing Cellular Automata
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You can choose two cellular automata (CA) of radius one and two colors, one of which is white. You can also choose an initial condition for each CA. When the CAs evolve and interact, some rule is chosen that defines the interaction; this can be either random (by default) or you can explicitly select an interaction rule. You can see how the two CAs compete and struggle for survival.
Contributed by: Eduardo Hermo-Reyes and Joost J. Joosten (June 2014)
(Department of Logic, History, and Philosophy of Science, University of Barcelona, Spain)
Open content licensed under CC BY-NC-SA
Reference  relates the set-up of this Demonstration to biological evolution while [2, 3] discusses the dependence on the initial conditions and how simple behavior relates to complex behavior.
 J. J. Joosten, "Complexity Fits the Fittest," Emergence, Complexity and Computation, 5, 2013 pp. 51–63. doi:10.1007/978-3-319-00254-5.
 H. Zenil and E. Villarreal. "Cellular Automata Sensitivity to Initial Conditions" from the Wolfram Demonstrations Project—A Wolfram Web Resource. demonstrations.wolfram.com/CellularAutomataSensitivityToInitialConditions.
 H. Zenil and E. Villarreal-Zapata, "Asymptotic Behaviour and Ratios of Complexity in Cellular Automata Rule Spaces," Journal of Bifurcation and Chaos, 23(9), 2013.
"Competing Cellular Automata"
Wolfram Demonstrations Project
Published: June 17 2014