Scaling, Renormalization, and Universality in Combinatorial Games: The Geometry of Chomp

: We develop a new approach to combinatorial games (e.g., chess, Go, checkers, Chomp, Nim) that unveils connections between such games and nonlinear phenomena commonly seen in nature: scaling behaviors, complex dynamics and chaos, growth and aggregation processes. Using the game of Chomp (as well as variants of the game of Nim) as prototypes, we discover that the game possesses an underlying geometric structure that “grows” (reminiscent of crystal growth), and show how this growth can be analyzed using a renormalization procedure. This approach not only allows us to answer some open questions about the game of Chomp, but opens a new line of attack for understanding (at least some) combinatorial games more generally through their underlying connection to nonlinear science. Combinatorial games, which include chess, Go, checkers, Chomp, dots-andboxes, and Nim, have both captivated and challenged mathematicians, computer scientists, and players alike (1-10). Analysis of these two-playe...

• Type: Conference
• Year: 2007
• Where: COCOA
• Authors: Eric J. Friedman, Adam Scott Landsberg
• Keywords: COCOA 2007, Combinatorial Games, Game, Nonlinear Phenomena