The Spirograph designs below are from a computer algorithm that calculates the hypotrochoid patterns for the 18 wheels and 2 rings in a standard Spirograph set. The algorithm generates designs in an endless sequence by selecting different wheels and rings for each design iteration.
In principle, these designs may be reproduced on paper with a Spirograph set. But in practice, the Spirograph cannot produce the fine detail needed for these designs, especially at pattern center.
This video shows how the designs are produced – pass by pass.