A Cellular Automaton for Blocking Queen Games
Matthew Cook, Urban Larsson, Turlough Neary

TL;DR
This paper demonstrates that the complex patterns of winning positions in Blocking Wythoff Nim, a two-player game involving queen moves and blocking, can be effectively modeled and analyzed using cellular automata, revealing self-organized chaotic structures.
Contribution
It introduces a cellular automaton model to analyze the intricate patterns of winning positions in Blocking Wythoff Nim, highlighting self-organization and chaos at large parameter values.
Findings
Winning position patterns can be computed by cellular automata.
Large k patterns exhibit self-organization and chaos.
Patterns become independent of k as it grows large.
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 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 is a parameter that defines the game, and the pattern of winning positions can be very sensitive to . As becomes large, parts of the pattern of winning positions converge to recurring chaotic patterns that are independent of . The patterns for large display an unprecedented amount of self-organization at many scales, and here we attempt to describe the self-organized…
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