As a child a favourite toy was my Spirograph with which I could generate endless pretty curves! Speaking of my favourite toy, there is a wonderful electronic version available.

The Nrich problem ‘Making Maths: Planet Paths‘ challenges students to draw some planet paths using a Spirograph. In case there is no Spirograph to hand they give instructions for making a simple one.


Spirograph – Desmos

Alternatively try an online version. Try Spirograph on the Desmos Graphing calculator.

This applet from wordsmith.org (requires Java) allows you to have the moving circle either inside or outside the fixed circle. You can alter various parameters and experiment.

From mathplayground.com comes this very clear and easy to use applet (the moving circle is outside the fixed circle).

Spirograph - Autograph Activity

Spirograph – Autograph Activity by Owen Elton

Owen Elton has written an excellent Spirograph Autograph activity (see Simon’s comment below) and also available on the Autograph player a very impressive 3D Spirograph!

For GeoGebra fans there are various applets available, including this which allows colour changes.