Open access
Date
2017-09Type
- Journal Article
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 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. This paper extends a previous study (Cook et al. in Cellular automata and discrete complex systems, AUTOMATA 2015, Lecture Notes in Computer Science, vol 9099, pp 71–84, 2015), containing further analysis and new insights into the long term behaviour and structures generated by our blocking queen cellular automaton. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000191144Publication status
publishedExternal links
Journal / series
Natural ComputingVolume
Pages / Article No.
Publisher
SpringerSubject
Blocking Wythoff Nim; Self-organization; Cellular automata; Wythoff NimOrganisational unit
02533 - Institut für Neuroinformatik / Institute of Neuroinformatics
Notes
It was possible to publish this article open access thanks to a Swiss National Licence with the publisher.More
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