>[!abstract] >The Feigenbaum constant ($\delta \approx 4.6692$) is a mathematical constant that describes the limit of the ratio of the distances between successive bifurcation points in a period-doubling cascade that leads to chaos. It is a fundamental constant in chaos theory, indicative of a universal behavior found in various dynamical systems, such as the [[logistic map]]. Other maps also reproduce this ratio; in this sense, the Feigenbaum constant $\delta$ in bifurcation theory is analogous to $π$ in geometry and $e$ in calculus. >[!related] >- **North** (upstream): [[Bifurcation theory]] >- **West** (similar): [[Logistic map]] >- **East** (different): — >- **South** (downstream): —