I found two definitions for guilloche, or guilloché (etymology unknown: possibly named for a carving tool devised by a French engineer named Guillot). First: "architectural ornamentation resembling braided or interlaced ribbons." As in this example from Assyria, 9th century B.C.:
Or this, from a more recent skyscraper in Chicago:
But guilloché is familiar to anyone who has studied a dollar bill
or taken a close look at a high-end watch face
In the latter case, it's simply decorative; in the former, it serves security purposes.
According to Wikipedia, guilloche "is a decorative technique in which a very precise, intricate and repetitive pattern is mechanically engraved into an underlying material via engine turning, which uses a machine of the same name, also called a rose engine lathe."
I found a gentleman named Ben Hodosi online who offers up contemporary guilloche designs as "security graphics."
Here are a few more examples:
Guilloche: the serious answer to the spirograph.
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