List questions from iterated-function-system | MathQA

Are there "half step", or other subdivisions, of the Mandelbrot iteration function?

Published on 16 Oct 2021 - 13:29

Are there known points on the boundary of the Mandelbrot set which iterate forever?

Published on 16 Oct 2021 - 13:36

Chaos game and fractal polygons

Published on 23 Feb 2026 - 17:24

If $f(f(x)) = x+1, f(x+1) = f(x) + 1$, is it true that $f(x) = x + 1/2$?

Published on 04 Nov 2021 - 13:16

Fourier series of iterated sin / Diagonalization of an infinite matrix of Bessel functions

Published on 05 Nov 2021 - 9:50

$ f(f(f(x))) = x $ with $ f(x) \ne x $ and $ f(f(x)) \ne x$

Published on 06 Nov 2021 - 8:21

Notational differences b/w Iterated functions & exponentiation.

Published on 23 Dec 2021 - 0:58

For any composition sequence $s$ of maps $h(X)=X/2, \ f(X)=(3X + 1)/2$, there exists an integer $X$ such that its Collatz sequence contains $s$

Published on 23 Feb 2022 - 3:47

Derivative of an iterative vector function?

Published on 21 Jun 2022 - 3:21

Iterated function with $a_{n} = {F^{2n}(1)} $ and $b_{n} = {F^{2n+1}(1) }$. How to show that $a_n$ is increasing and $b_n$ is decreasing?

Published on 24 Nov 2022 - 15:52