Last edited 12dec2013 by ajmori2@illinois.edu
Find this document at http://new.math.uiuc.edu/math198/ajmori2

# Alec Mori's Attempt at Changing the Westergame

## Abstract

I am attempting to turn the structure made by Chang Hon for the quasicrystals into a game.

In this RTICA, the user sees a series of rhombuses (faces) that share edges, a graph with 15 nodes, and a series of instructions. By bracing a certain number of the faces, one hopes to fully brace the shape, such that you cannot bend the shape along any blue line (ribbon)

## The game itself

To start the game, one simply goes to the folder that the game is in (in this case, the path is ajmori2/moripy2mini) and runs the command "python theWesterGame.py" in the terminal. This should launch a screen that looks extremely similar to this

So, clicking with left mouse button on the structure on the left hand side of the screen (the quasicrystal), you can select some of the faces of the quasicrystal. After doing so, you can press enter to make the faces unalterable, outside of rotating them (braced). I did this by transforming every line segment of each rhombus into a different line, each with the formula "y = mx + b". I then found the location of where the user clicked and checked between which set of lines it was in. By hitting the enter button, it turns the corresponding face green (deselecting also uses enter, and returns the color to white).

Clicking with right button allows you to select a ribbon, highlighting it a lighter color of blue. Once you select a ribbon, you can rotate it right or left by clicking the ',' and '.' keys, respectively, In order to do this, I turned each ribbon fragment into a line with the equation "y = mx + b". However, because the lines go on infinitely and the segments are segments, I needed to ensure the mouse click was also in the general vicinity of the line itself - thus, I also made sure it was within a few units of the endpoints as well. After rotating, the structure could look something like this

The graph on the right side of the screen has nodes that represent each ribbon, and edges that represent the intersection of two ribbons. If the face is at which two points intersect is selected, the edge is drawn red - else, it is drawn grey. The WesterGame is "won" when it has been minimally fully braced. The quasicrystal if fully braced if the graph on the right is connected (all nodes can be traversed by walking along the red edges). The minimum number of highlighted edges needed for it to be braced is 14. Best of luck!