Title

Collaborative Game Mosaics

Degree Year

2021

Document Type

Thesis

Degree Name

Bachelor of Arts

Department

Mathematics

Advisor(s)

Robert Bosch

Keywords

Mosaic, Games

Abstract

Imagine two players are playing a strategy board game. With one player holding black stones and the other player holding white stones, they take turns to place their pieces. After a while, they start to recognize some patterns. With three colors in front of them, black, white, and the color of the game board, they are curious about if they can form a recognizable image. Instead of playing the game to win, they start to collaborate with each other to form a mosaic. Later, they invite more players and provide them their own stones in different shades of gray. The goal of this project is to use mathematical optimization techniques to design mosaics that simultaneously resemble well-known images and look like the current state of a board game like Gomoku or something that could be played on a Go board or chessboard. The work described here builds upon techniques devised by Professor Robert Bosch and some of his students. The paper will be structured as follows: First, we will discuss the data, variables, objective function, and universal constraints. Then we will explore constraints for two specific games, Gomoku and chess. Next, we will present several examples, sharing both images and statistics, and we will talk about methods we have devised for improving the results. We will conclude with a discussion of future directions for our research.

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