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, macOS, Windows
Deutsch ελληνικά English español suomi français italiano 日本語 한국어 Nederlands português русский tiếng Việt 简体中文 繁體中文
KaleidoPaint icon
Create colorful symmetrical paintings based on the 17 tiling patterns.
العربية Deutsch English español français italiano 日本語 Nederlands português русский 简体中文 繁體中文
KaleidoTile icon
Explore polyhedra and tessellations while creating colorful works of art.
iOS, macOS, 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).
iOS, macOS, Windows
English español français italiano 日本語 português Türkçe 简体中文 繁體中文
4D Maze icon
4D Maze
Have fun solving 4D mazes (for everyone).
iOS, macOS, Windows
Deutsch English italiano 日本語 português русский Türkçe
4D Draw icon
4D Draw
Draw simple 4D figures (for geometry students).
iOS, macOS
English italiano português
Crystal Flight icon
Crystal Flight
Fly freely in crystals (for everyone).
iOS, macOS
English italiano português

Other Resources

Shape of Space icon
The Shape of Space 3rd edition English
A gentle introduction to topology and geometry, with full-color figures throughout.
Hyperbolic Blanket icon
How to Sew a Hyperbolic Blanket العربية English 日本語
Step-by-step instructions for sewing a hyperbolic surface from fleece.
Hyperbolic Games
Non-Euclidean billiards in VR
Body coherence in curved-space virtual reality games

Recent Updates

2022-10-10 KaleidoPaint
Entire app re-written in Swift and SwiftUI.
File browser lets you organize your drawings into folders.
File browser supports iCloud Drive as well as local storage on device.
Color picker offers a choice of five color selection methods (grid, spectrum, sliders, eyedropper or hex code) and a user-customizable saved-color palette.
Separate line color ("paintbrush") and fill color ("paint bucket").
You can copy the color of any dot, line or filled region directly to the paintbrush, the paint bucket or any other dot, line or filled region.
You can copy the thickness of any dot or line directly to the paintbrush or any other dot or line.
Options to "change all of same color", "change all of same thickness" or "delete all of same color".
Exports images to any folder.
Option to export images with transparent background.
Adjustable parameter for less vigorous or more vigorous line smoothing.
Simple slider-based interface to adjust drawing's aspect ratio and shear.
Default grid alignment is now consistent among the symmetry patterns *2222, 2222, 2*22, 22*, 22×, **, *× and ××, in the sense that mirror lines and rotation points agree, to make it easier to see the relationships among those symmetry patterns.
Symmetry panel now positions the buttons for the families (**, *× and ××), (22*, 22×) and (*2222, 2222, 2*22) consistently, so you can easily see what symmetries change and what symmetries stay the same as you switch from one pattern to a different pattern in the same family. This also lets you see how the drawing's symmetries relate to the pattern's name in orbifold notation.
Many thanks to Francine Champagne, Amber van Hoek and Geneviève Crabe for their extensive help improving KaleidoPaint. KaleidoPaint is far better thanks to their ideas.
Special thanks to Francine for creating the icons for the symmetry pattern buttons as well as for her instructional videos and web pages.
Special thanks to Amber for creating KaleidoPaint's elegant icon and for providing spectacularly good drawings for KaleidoPaint's App Store screenshots.

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Contact Jeff Weeks