I sat in on the last 10 minutes (I had crappy luck with my session selection) of a presentation at T

^{3}this past weekend that reminded me of Recursive Explorations With Number Cycles.

The sketch below is based on the iterative rule

which has been modified to be

Under certain conditions, it appears that the points might lie on a hyperbola. At other times, it appears the points might lie on some sort of cubic. Certainly, an investigation is in order!

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