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.

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!

On GeoGebra, there are various applets available, for example:

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