You subtly referenced one of my favorite facts. "In 1920, Pierre Fatou expressed the conjecture that -- except for special cases -- all critical points of a ra

You subtly referenced one of my favorite facts. "In 1920, Pierre Fatou expressed the conjecture that -- except for special cases -- all critical points of a rational map of the Riemann sphere tend to periodic orbits under iteration. ... can be interpreted to mean that for a dense set of parameters 'a', an attracting periodic orbit exists [in the logistic map]." Friggin' blew my mind at age 20. Still kinda does. :)