Strange attractor

A strange attractor is an attractor of a dynamical system that is simultaneously geometrically complex (typically a fractal) and dynamically unstable. Unlike fixed points and limit cycles, which are simple and predictable, a strange attractor confines trajectories to a bounded region of state space while ensuring that any two nearby trajectories diverge exponentially. This marriage of order and disorder is the defining geometry of chaos.

The term was coined by David Ruelle and Floris Takens in 1971 to describe the attractors they believed underpinned fluid turbulence. The Lorenz attractor — a butterfly-shaped set of trajectories in a three-dimensional atmospheric model — is the iconic example. Strange attractors are not rare mathematical curiosities; they appear in weather, neural dynamics, cardiac rhythms, and financial markets wherever nonlinearity and feedback interact at suitable parameter values.