ELI5:
Imagine some sort of a polynomial function f(x) = r * x * (1-x)
that is also depending on some constant r
in range 0 < r < 1
.
You apply x = f(x)
for many times, at your wish. Think of it as a for-loop, or f(f(f(…f(f(x))…))). The resulting value will reside (converge) to some value.
So, this looped function sets to some stable point with any r
in range until x < 3
. After that, it doesn’t converge but it will constantly jump between one of 2 points, then 4, 8, … and at some point it goes wacky-macky.
The graph from Wikipedia merely shows the probability of the value f(f(f(...f(f(x))...)))
for all r
in the given range.
If you’re curious, Veritasium’s made a good explanation here: https://youtu.be/ovJcsL7vyrk
Okay. I declare tomorrow to be International throw imperial units day.