Jeff Weeks’

Topology and Geometry Software

Torus Games icon
Torus Games
Eight familiar games introduce children age 10 and up to the concept of a finite yet unbounded universe.
iOS, Android, Mac, Windows
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KaleidoPaint icon
KaleidoPaint
Create colorful symmetrical paintings based on the 17 tiling patterns.
iOS, Android
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KaleidoTile icon
KaleidoTile
Explore polyhedra and tessellations while creating colorful works of art.
Mac, Windows
Cymraeg English français italiano 日本語 한국어 português 简体中文 繁體中文
Curved Spaces icon
Curved Spaces
Fly in a multiconnected universe (for math and physics students).
Mac, Windows
English español français 日本語 简体中文 繁體中文
4D Maze icon
4D Maze
Have fun solving 4D mazes (for everyone).
iOS, Android, Mac, Windows
Deutsch English italiano 日本語 русский
4D Draw icon
4D Draw
Draw simple 4D figures (for geometry students).
iOS, Android, Mac
English

Recent Updates

2017-10-31 KaleidoPaint
(iOS) Graphics rewritten using Apple's “Metal” graphics library, with fallback to OpenGL ES on older devices (pre-A7) or on iOS 9.
(iOS) Computes flood-fills directly on the GPU. Makes use of the GPU's parallel processing capabilities to achieve a 2-fold to 24-fold speed-up, depending on number of symmetries in the particular wallpaper group. (Metal version only)
(iOS) KaleidoPaint's memory demands have been reduced 1000-fold by storing flood-fills using run-length encoding (RLE) instead of raw bitmaps. For example, at Medium Resolution, each filled region required a 1 MB mask in the previous version of KaleidoPaint, but in the new version the same filled region requires only ~1 KB. (Metal version only)
(iOS) Redraws flood-fills from RLE data directly on the GPU, making full use of the GPU's parallel processing capabilities. (Metal version only)
(iOS) Added High Resolution. (Metal version only)
(iOS) Improved support for iPencil and other stylus input. Thanks to Francine Champagne for reporting this issue.
(iOS) Fixed bug that was causing slowly-drawn lines to retain too many nodes. Again, thanks to Francine Champagne for reporting this bug.
(iOS) Adjusts input touches so that the curve-in-progress will appear even when the user starts drawing in a distant translate of the main unit cell. Thanks to Jeff Racinski for reporting this bug.
2017-10-29 Torus Games
(iOS) Reorganized sound effects playback to avoid unwanted hesitations in animations.

Other Resources

Kali icon Kali
Children of all ages create beautiful art based on the 17 tiling patterns.
Move & Turn icon Move & Turn
Transform any Platonic or Archimedean solid into any other.
Hyperbolic Blanket icon How to Sew a Hyperbolic Blanket
Step-by-step instructions for sewing a hyperbolic surface from fleece.
Hyperbolic Games icon Hyperbolic Games
Play Sudoku, Pool and Maze on hyperbolic surfaces (for undergraduate geometry classes).
SnapPea icon SnapPea
Create and study 3-manifolds (for researchers).

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Contact Jeff Weeks

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.