Spirographs, Lissajous figures, rose curves — curves traced by moving points.
An interactive piece that redraws any closed shape — a freehand drawing, an uploaded image, or the outline of a country or city — with a chain of spinning circles. You can change the number of circles to see how the approximation improves, and display the spectrum of circle sizes and the breakdown into sine waves in x and y. Circles riding on circles is the same idea that drives spirograph curves.
The home of a program for drawing mathematical knots and links in three and four dimensions and reshaping them interactively, with a gallery of images made with it. Available for Windows, macOS and Linux — a tool for treating knots as closed curves to shape.
A collection of musical toys to play in the browser. Musical Spirograph turns a spirograph into musical patterns; others include pendulum waves, Polyrhythm with its polygons, Cellular Sequencer built on the Game of Life, and Wave Drawer for drawing a waveform and hearing it — many let you see and hear a mathematical mechanism at work.
A personal site with a vast collection of notes and examples on geometry, fractals, curves and surfaces, visualisation and dome projection. Equations sit alongside code, making it a long-standing reference for makers.