Algebraic agents playing board games - Visualization of algebraic systems for Kansei

点击翻译按钮获取中文摘要

The purpose of this research is to provide a first step towards formulating a framework for understanding algebras in terms of Kansei engineering by letting elements in some algebraic systems play board games. We call such elements algebraic agents. We confine ourselves to a kind of board games with n*n squares (cells) arranged in an n-by-n grid. There are two or more teams of elements with their characteristic algebraic operations. For example, two teams of integers whose operations are addition and multiplication, respectively. Each agent can move from one cell to other cell. When two algebraic agents encounter, their fight starts. They win or lose the fight by means of their own operations. Then the winner survives and the loser disappears or is transferred to his opposing team. Finally the team which defeats all agents in other teams gains a victory.