Dear Professor,
I found a very small analytical function. It calculates the same result as Feigenbaum Scenario.
I.e. formula 15 in the article (M. J. Feigenbaum, Universal behavior in nonlinear systems, Physica 7D (1983) 16-39).
x(i+1)= 4*lambda*x(i)*{1-x(i)}
So, we will use y = f(x).
It was amazing.
Do you know about this function? If not, and if you need it, I can make a gift as a volunteer.