If you travel far enough in a straight line on a torus you will eventually end up back where you started. This is because the torus "wraps around" to meet itself. For example, the left and right sides of the square are both red, meaning that an object located at the left edge of the square is, somehow, also simultaneously located at the right edge. In this picture, edges with the same color are meant to represent the same points in space. In the case of the torus, we can draw this as a parallelogram whose opposite sides are identified with each other, like in the following picture: One useful way of describing how a topological surface connects to itself is through use of its fundamental polygon. It is also fairly easy to program around, since in general it just requires resetting the coordinates of an object that moves off of the screen so that it reappears at the other side.
The torus is one of the simplest topological spaces to understand (outside of the disk and the Euclidean plane). My goal with this project was to do something along the lines of Torus Games, but to explore more exotic topological spaces than just the torus, and to do so using an action game rather than a puzzle game. Whereas most board games that we are used to have finite boundaries, on a torus the edges "wrap around", and things that leave through one edge seem to reappear at the opposite edge. Torus Games allows players to explore how familiar games work differently when space connects to itself differently. Jeff has an entire website devoted to interesting games and other interactive programs for illustrating abstract mathematical concepts, and anyone who knows me knows that I'm all about that. This project was largely inspired by the freeware program Torus Games, by Jeff Weeks.
CREATING SCREEN WRAP ROOM IN GML FREE
Please feel free to modify it in any way you wish.
CREATING SCREEN WRAP ROOM IN GML FOR FREE
It is available for free at my itch.io page, and the source code is available under the MIT license at my GitHub page. Whatever educational merit it may have, I mostly just made it as a way of getting back into my younger self's hobby of independent game design after finishing grad school.
This game was developed in GameMaker Studio 2. In order to better view these two interpretations, the camera can be adjusted to either remain fixed in space or follow the player. It is possible to interpret each space as either consisting of a single screen whose edges connect to each other, or as an infinite array of tiles that fill the Euclidean plane.
All of these spaces wrap around in one or two directions, but some of them mirror or rotate objects as they move across edges, meaning that the player (and their controls) can become mirrored. In this variant of the game, the player can choose from six different topological surfaces (the torus, Klein bottle, sphere, real projective plane, cylinder, and Möbius strip) to play on. The original arcade game takes place on a torus, with both the player's ship and the asteroids wrapping around from one side of the screen to the other, requiring the player to develop an intuitive understanding of how the game's space connects to itself in order to effectively play. This is a game based on the classic 1979 Atari arcade game Asteroids, in which the player controls a ship and attempts to avoid and destroy asteroids floating around in space. Steepest Descent Papercraft Cookery Links Topological Asteroids
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