Curved Spaces Icon Curved Spaces

Curved Spaces screenshot

Curved Spaces is a flight simulator for multiconnected universes. Because light itself wraps around such a space, inhabitants see their universe’s contents repeating in a crystalline pattern, like a hall of mirrors but with no reflection.

Curved Spaces is intended for undergraduates and graduate students studying 3‑manifolds, and has also found use as a research tool in topology and cosmology. Recreational math enthusiasts may instead prefer Torus Games, which offers 3D Mazes and 3D Tic-Tac-Toe in a variety of multi-connected 3D spaces, along with games on multi-connected 2D surfaces.

English, French, Chinese (simplified), Chinese (traditional)
Last update
13 November 2018 (Version 4.1.1)
Faster tiling and culling algorithms
(iOS) Updated for iOS 11 and 12
(iOS) Ignores random vibrations when phone or tablet is lying still, to avoid needless animation and save energy
(macOS) Updated for macOS 10.13 and 10.14

Contact Jeff Weeks.

With deepest thanks to the translators for their thorough, careful and most professional translation of Curved Spaces:
Alberto Pino Blanco, Roland Lehoucq, 竹内建 (Tatsu Takeuchi), 邹燕清 (Yanqing Zou).

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This material is based upon work supported by the National Science Foundation under Grant No. 1503701. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.

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