Chaos Made Visible: Active particles trace Lorenz-like attractors in physical space

Abstract

Chaotic attractors are typically visualized in an abstract phase space. Here we show that an orientable active particle moving through a steady, two-dimensional, multivortex flow can trace a Lorenz-like chaotic attractor in its real space trajectory. Despite the flow being strictly time independent, coupling between particle position and orientation creates a three-dimensional nonlinear dynamical system. For suitable particle shape and swimming speed, the trajectory organizes into a striking two-lobed geometry reminiscent of the classical Lorenz attractor. A structured first return map, positive largest Lyapunov exponent, and a broadband power spectrum establish that the underlying motion is chaotic. Varying the swimming speed reveals a rich sequence of dynamical regimes as self-propulsion breaks streamline confinement and reorganizes the particle motion. Our results demonstrate how an internal orientational degree of freedom can make chaotic dynamics directly visible in physical space, allowing a single active particle to trace a chaotic attractor as it moves through an otherwise steady flow.