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.
Related
- Geodesic Trapping and Escape of Active Particles on Curved Surfaces
- Morphological instability and negative geometric friction from contact with active and driven particles
- Emergent Self-Organisation of Intelligent Active Particles
- Partial Entropy production of active particles with hidden states in potentials
- Inferring interactions between active particles using harmonic traps
BibTeX
@misc{valani2026chaos,
title = {{Chaos Made Visible: Active particles trace Lorenz-like attractors in physical space}},
author = {Rahil N. Valani and Ekashman Tiwari and Aritra Roy},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32640},
eprint = {2610.32640},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32640},
}
RIS
TY - UNPB
TI - Chaos Made Visible: Active particles trace Lorenz-like attractors in physical space
AU - Rahil N. Valani
AU - Ekashman Tiwari
AU - Aritra Roy
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32640
UR - https://arxiv.org/abs/2610.32640
AB - 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.
ER -