Feigenbaum function
In the study of dynamical systems the term Feigenbaum function has been used to describe two different functions introduced by the physicist Mitchell Feigenbaum: the solution to the Feigenbaum-Cvitanović functional equation; and the scaling function that described the covers of the attractor of the logistic map == Idea == === Period-doubling route to chaos === In the logistic map, we have a function f r ( x ) = r x ( 1 − x ) {\displaystyle f_{r}(x)=rx(1-x)} , and we want to study what happens when we iterate the map many times. The map might fall into a fixed point, a fixed cycle, or chaos.