Create a floor subdivided into many intersecting discs. Each disc turns sometimes and stops sometimes to allow other discs to turn. Cuts in one disc will need to line up properly to allow an intersecting disc to turn.
The Geranium Puzzle illustrates the concept.
Inspired by a club with a slowly rotating dance floor, a single disc. Multiple slowly rotating discs might make more mixing happen. Of course, stuff getting caught in the cracks will be a problem.
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