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2005, 2005(Special): 453-462. doi: 10.3934/proc.2005.2005.453

## Nim-induced dynamical systems over Z2

 1 Montclair State University, Department of Mathematical Sciences, Upper Montclair, NJ 07043, United States 2 Department of Mathematical Sciences, Montclair State University, Upper Montclair, NJ 07043, United States

Received  September 2004 Revised  April 2005 Published  September 2005

Winning and losing positions in the well-known two-player game, Nim, are defined recursively as a two symbol sequence depending on a $k$-parameter set known as the subtraction set. In this paper, we write the recursion as a nonlinear dynamical system defined on the phase space $\mathbb Z_2^{s_k}$ with the binary sequence for Nim generated by the appropriate initial conditions. The transient dynamics and Garden of Eden points are completely determined for arbitrary-sized subtraction sets. A characterization of cycle lengths for two parameter subtraction sets is determined. Extensions of the two parameter case to an arbitrary-sized subtraction set are explored.
Citation: Michael A. Jones, Diana M. Thomas. Nim-induced dynamical systems over Z2. Conference Publications, 2005, 2005 (Special) : 453-462. doi: 10.3934/proc.2005.2005.453
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