There really aren’t that many spirograph designs that can be made with LEGO, because there are a limited number of gears and they mostly have the same tooth counts–the smaller ones sport 8 ...

Spirographs, invented in 1962, are toys that create geometric patterns using gears. These designs are used in art and similar patterns can be found in nature.

Spirographs can make some pretty groovy designs on paper ... starts with a quick proof-of-concept using an actual plastic Spirograph toy to make sure it isn’t a totally unworkable idea.