Similar to changing a game’s dimensionality, changing the Graph Space of a game can dramatically altar the underlying rule construct. A significant amount of innovations in game design over the last several decades had been driven by this exact practice. The number of topological variations on Tetris is massive, with seemingly minor alterations in the pieces or playspace creating massively different games.
In his 2014 GDC talk, Raph Koster points out a couple non obvious examples of interesting topologies in popular games:
- Asteroids is not played on a square, but rather a donut.
- Pacman is either a donut or mobius strip, depending on the specific level.
- Snakes & Ladders is half-jokingly describe as Non-Euclidean Geometry with wormholes.
Practical Creativity by Raph Koster, GDC 2014 Koster’s Taxonomy of Games Topology