196

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