BEYOND EUCLIDEAN BOUNDARIES: ANALYZING NON-EUCLIDEAN SPACES IN GAMES (Proceedings of the World Conference on Media and Mass Communication, 2025)
Game space is a reproduction of physical space; however, it is not constrained by the same limitations. We live in an Euclidean space, where geometry follows consistent rules: parallel lines never meet, angles in a triangle always sum to 180 degrees, and distances are fixed. However, non-Euclidean spaces break Euclid's fifth postulate with the result that parallel lines can converge or diverge, and distances may stretch or warp, as demonstrated in games like Portal and Antichamber.  By going beyond these constraints, non-Euclidean spaces offer new possibilities for advancing a game's narration, aesthetics, and mechanics. The potential of non-Euclidean games has started to be discovered, but there has yet to be a definitive framework. Such a framework could unify the understanding of non-Euclidean mechanics, bridging theory and practical applications to enrich game design by stimulating innovativeness. The present work examines the possibilities of non-Euclidean spaces, particularly in relation to game mechanics. To this end, we analyzed ten games that feature diverse spatial qualities. Each game represents a different non-Euclidean space type. Schell's categories of mechanics are used as a conceptual structure for the analysis. The first category is space; the others are time, objects, actions, rules, skills, and chance. We examined the correlation between non-euclidean space and other categories to uncover the influence of non-euclidean spaces in games. Our findings show that non-Euclidean spaces offer new ways to build novel interactions and relations. It demonstrates the short comings of existing game space type classification and extends our understanding of spatial structures in games. This expanded knowledge has the potential to lead to richer gameplay experiences.
Keywords: game design; non-euclidean spaces; game mechanics; level design; game analysis