Once the bifurcation diagram has been plotted ($x_{n+1}=rx_n(1-x_n)$), there are 3 elements or properties that I don't know haw to explain, and I have not found any article where they are explored. Those are:
- Islands of stability; or the spaced ranges where the function stops it's chaotic behaviour and has a reduced number of values again[1].
- High concentration points: overall, the extremes of the bifurcation diagram are darker, which means the limit of $x_{n+1}=rx_n(1-x_n)$ when $n$ tends to $\infty$ and $x_0$ is random, is more likely to be either very large or very small. However, there is a specific value of $r$ (3.68) in which the higher concentration is in the middle of the Y-axis of the graph, rather than in the extremes. What determines the minimum and maximum values of the limit, and their likely-ness. The darker areas=higher concentration of points=higher chance for the limit to have said value, but how and why?[2]
- Inner curves: what do they represent? how are they formed? [3]
