Reminds me of some cylindrical contraption I saw at the Exploratorium in San Francisco over a decade ago. I believe too it was described even earlier in a "Scientific American" column — either Mathematical Recreations or Computer Recreations.

It was some kind of device where a large horizontal cylinder was perhaps covered with numbers? Maybe there were rings or some other kind of "cursor" on the contraption? And I think as you rotated it there was some kind of math performed and, like this "6174" thing, it would seem to converge on a single number after so many iterations regardless of the starting state.

Wish I could remember what that was.