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A cellular automaton for blocking queen games

descriptionPublicationkeyboard_double_arrow_right Article , Part of book or chapter of book , Preprint , Conference object 01 Jan 2015Embargo end date: 01 Jan 2015 Switzerland English Publisher:Springer Science and Business Media LLCJournal:Natural Computing, volume 16, pages 397-410 (issn: 1567-7818, eissn: 1572-9796,

Authors: Cook Matthew; Larsson Urban; Neary Turlough;

doi: 10.1007/s11047-016-9581-2 , 10.1007/978-3-662-47221-7_6 , 10.48550/arxiv.1506.01431 , 10.3929/ethz-b-000191144

arXiv: http://arxiv.org/abs/1506.01431

handle: 20.500.11850/191144

A cellular automaton for blocking queen games

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Abstract

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 {\em 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.

14 pages, 12 figures, 21st IFIP WG 1.5 International Workshop, AUTOMATA 2015, Turku, Finland, June 8-10, 2015

Country

Switzerland

Related Organizations

ETH Zurich
Switzerland
Institute of Neuroinformatics UZH + ETH Zurich
Switzerland
Dalhousie University
Canada
Institute of Neuroinformatics
Switzerland
Language Center of UZH and ETH Zürich
Switzerland

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Keywords

Self-organization, Cellular automata, Dynamical Systems (math.DS), [INFO] Computer Science [cs], Blocking Wythoff Nim; Self-organization; Cellular automata; Wythoff Nim, Wythoff Nim, 1706 Computer Science Applications, FOS: Mathematics, 570 Life sciences; biology, Mathematics - Combinatorics, 1700 General Computer Science, Combinatorics (math.CO), Mathematics - Dynamical Systems, Blocking Wythoff Nim, 2614 Theoretical Computer Science, 68Q80, 91A46, 10194 Institute of Neuroinformatics

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