Guilloché Patterns

"A guilloché pattern might be very close to you at the moment. Paper banknotes,
passports, identification cards, certificates, checks, bonds, and warranties all
frequently feature guilloché pattern. In figure 1, the elaborate lines are an
example of such a pattern.

You may have made a guilloché pattern yourself. In 1962, Denys Fisher
was designing bomb detonators for NATO, and his research inspired him to invent
spirograph (I frankly don’t see the connection, myself). Although considered a
child’s toy, the spirograph has some serious math behind it. The patterns the
toy produces, called epitrochoids, have been studied by Dürer, Desargues,
Leibniz, Newton, L’Hospital, Bernoulli, and Euler. They belong to a class of
curves called roulettes…"