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We show that the full features of the dynamics towards the Feigenbaumattractor, present in all low-dimensional maps with a unimodal leadingcomponent, form a hierarchical construction with modular organization thatleads to a clear-cut emergent property. This well-known nonlinear model systemcombines a simple and precise definition, an intricate nested hierarchicaldynamical structure, and emergence of a power-law dynamical property absent inthe exponential-law that governs the dynamics within the modules. This classicnonlinear system is put forward as a working example for complex collectivebehavior.

A dynamical model for hierarchy and modular organization: The trajectories en route to the attractor at the transition to chaos