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In this paper we discuss computer simulations of de Sitter and anti de Sitterspacetimes, which are maximally symmetric, relativistic analogs ofnon-Euclidean geometries. We present prototype games played in thesespacetimes; such games and visualizations can help the players gain intuitionabout these spacetimes. We discuss the technical challenges in creating suchsimulations, and discuss the geometric and relativistic effects that can bewitnessed by the players.

Simulating, Visualizing and Playing with de Sitter and anti de Sitter spacetime