This is my first time here as I'm investigating fractals.
I started of by writing about the similarity between a bifrucation diagram of a population, using formula $z_{n}=a*z_{n-1}*(1-z_{n-1})$.
I ended up getting the following image:bifurcation diagram
I compared this to the mendelbrot set, without seeing to much similarity at first, but in a youtube video, I saw that there 2 are very similar, when placed on top of eachother:Mendelbrot set, placed on bifurcation diagram
What could be a way of explaining the way that the periodic behaviour of both graphs are similar if not identical? By taking the fracture of the lengths I discovered the Feigenbaum constant, 4,669... (as expected), though I was curious if there is another explanation for this behaviour.
Thank you all in advance.
Greetings! Have a nice day!
There is a simple change of coordinates between $x \to r x (1 - x)$ (Logistic Map) and $y \to y^2 + c$ (Mandelbrot set): $$c=\frac{1-(1-r)^2}{4}$$ $$r = 1 + \sqrt{1 - 4 c}$$
Reference: https://en.wikipedia.org/wiki/Talk:Logistic_map#Very_old_discussions