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Guilloche patterns --- slightly off group topic

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  • Subject: [mg39436] Guilloche patterns --- slightly off group topic
  • From: "DIAMOND Mark R." <dot at>
  • Date: Sat, 15 Feb 2003 01:42:04 -0500 (EST)
  • Organization: The University of Western Australia
  • Sender: owner-wri-mathgroup at

I hope there is no objection to my reposting this (originally
alt.math.recreational) here.

I wondered if anyone might be able to shed some light on the construction of
Guilloche patterns. I have had a look at the entry on Mathworld
and also seen the Mathematica notebook, but neither really give much
about the construction. The notebook, for example, produces a series of
interesting guilloche patterns, but gives no information about the multitude
of parameters in the equations.

Additional questions I have are (1) are all the standard mathematical
constructions of guilloche patterns based on sine waves, and if not, what
other forms are there? (2) was there an explicit mathematical basis for the
construction of traditional guilloche patterns? (2a) if so, what was it?
(2b) if not, are there implicit rules that can be easily infered from the
traditional designs?

Last of all, can anyone suggest a reference (a paper book would be nice!)
that discusses traditional guilloche designs. I am really interested in
discovering more. I have, of course, looked at the other sites referenced in
the Mathworld entry.


Mark R. Diamond

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