Re: [math-fun] Interesting limit question (sort of spoiler alert)

On 06/09/2020 01:07, Allan Wechsler wrote:

Note that the set of Foias points looks much more like a Julia set than it does like a Mandelbrot set, which makes sense because it is asking about the divergence of a *single* iterated function. I suspect that if we iterated (c + 1/f(n))^n (with an arbitrary constant c replacing 1 in the original), we would get a whole family of Julia sets plus a Mandelbrot analogue.

If you use a constant whose absolute value is > 1, then an "overlarge" x_n gives you (c + small)^n next, and that will be _large_ rather than _small_, so the nature of the behaviour is different in this case. (If the absolute value is < 1, maybe that's OK?) -- g