A Cellular Automaton for Blocking Queen Games

  • Matthew Cook
  • Urban Larsson
  • Turlough NearyEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9099)


We show that the winning positions of a certain type of two-player game form interesting patterns which often defy analysis, yet can be computed by a cellular automaton. The game, known as Blocking Wythoff Nim, consists of moving a queen as in chess, but always towards (0,0), and it may not be moved to any of \(k-1\) temporarily “blocked” positions specified on the previous turn by the other player. The game ends when a player wins by blocking all possible moves of the other player. The value of \(k\) is a parameter that defines the game, and the pattern of winning positions can be very sensitive to \(k\). As \(k\) becomes large, parts of the pattern of winning positions converge to recurring chaotic patterns that are independent of \(k\). The patterns for large \(k\) display an unprecedented amount of self-organization at many scales, and here we attempt to describe the self-organized structure that appears.


Cellular Automaton Outer Space Fibonacci Number Vertical Thickness Fabric Pattern 
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© IFIP International Federation for Information Processing 2015

Authors and Affiliations

  1. 1.Institute of NeuroinformaticsUniversity of Zürich and ETH ZürichZürichSwitzerland
  2. 2.Department of Mathematics and StatisticsDalhousie UniversityHalifaxCanada

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