The technique began as precision engraving in 16th–17th-century France and reached its peak with the "rose engine lathe" — a machine that combines rotational and oscillating motion to cut a metal plate. The resulting curves were too precise and too dense to reproduce by hand, which is exactly why they first decorated pocket-watch cases and fine jewellery (Fabergé eggs are the famous example).
That same "impossible to forge by hand" property is what made it the standard for security printing — banknotes, passports, cheques. Before computers, there was effectively no way to copy this pattern freehand without a rose engine of your own.
Structurally it's the same idea as a spirograph curve (a hypotrochoid): rotational motion with a sinusoidal oscillation layered on top. The demo overlaps three concentric-ring fields from different centre points and rotates them together slowly, so the three interfere and read as a dense, woven texture — the same "rotating overlaid patterns create interference" principle as the moiré entry, applied here to a security-print context.
When to use
Use for security/certificate-feel premium packaging, watch and jewellery branding, and UI backgrounds that metaphorically signal "tamper-proof."