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.
Alternatively, try an online version. Try Spirograph on the Desmos Graphing calculator.
On GeoGebra, there are various applets available, for example: