The Rose Lathe, its functions and operation ( 38 min video)

[DIYSwede]

Chuck Bommarito has got one of these unique ornamental lathes, amongst other machines and tools in his homeshop.
He runs a demo on it for the festive season:

[Toolmaker51]

Original inventor of rose engines is unclear, web-wise. But a useful, really critical function, was embellishing plates for printing currency, foiling counterfeiters. Karl Fabrege used them making his famous Egg decorations for the Tsar Alexander III of Russia. But Guilloché [very big 1700's France] ornate enameling has been found dating back to 1300's Cyprus. Originally hand cut, custom appearance of production items was possible via the rose engine.
No less, far back as they go; the complexity was born from mechanically oriented minds, slide rules, paper and pens.