一种求解阻塞皇后对策的元胞自动机
A Cellular Automaton for Blocking Queen Games
摘要：
我们表明，获胜的位置，某种类型的两个玩家的游戏形式有趣的模式，往往藐视分析，但可以计算的元胞自动机。该游戏被称为{ \em Blocking Wythoff Nim}，包括像国际象棋中那样移动皇后，但总是朝向（0，0），并且它可能不会被移动到其他玩家在前一轮指定的任何$k-1$临时“阻挡”位置。当一个玩家通过阻止另一个玩家的所有可能移动而获胜时，游戏结束。$k$的值是定义游戏的参数，获胜位置的模式可能对$k$非常敏感。随着$k$变大，获胜位置的部分模式收敛到独立于$k$的重复出现的混沌模式。大型$k$的模式在许多尺度上显示出前所未有的自组织量，在这里，我们试图描述出现的自组织结构。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
