The Spirograph toy that most people are familiar with produces regular, circular
patterns that are sometimes called Guilloché patterns. The concept dates
back as far as the 1700's and machines have been produced that can etch these
patterns in metal, wood or even glass. The patterns are sometimes used at the
background for stocks, bond, currency, checks and money orders because they are
difficult to counterfeit. Here is a generalized equation for producing Guilloché
Wikipedia Page with more information on Guilloché patterns.