I am very new to Mathematica. I am trying to draw an orbit diagram of the quadratic map $f(x) = r - x^2$ for $r <= 2$. I have the following idea for a program:
For each value of $r <= 2$:
- Iterate $f(x)$ starting with $x_0 = 0$ and store values in list.
- Plot the last elements of the list against $r$.
I am having a lot of trouble with the implementation. Hope you can help me!