---
tag: 7FWX24X5MW
kind: concept
name: Attractor
msc: [37C70, 37G35, 37B25]
sources:
  - url: https://en.wikipedia.org/wiki/Attractor
same_as:
  wikidata: Q507187
  wikipedia: Attractor
---

## Summary

An attractor of a dynamical system is an [[invariant set|WWZTW11664]] towards which all nearby states evolve.
It describes what one actually observes after a long time, since transients die out and the state settles near the attractor.
Attractors can be single points, closed orbits, tori, or sets with fractal structure, the [[strange attractors|9WKCZGG906]].
Several precise definitions are in use; they agree on simple examples and differ in how they treat attraction and indecomposability.
The [[global attractor|4SH2ZB984E]] of a dissipative system is a related notion that attracts every bounded set.

## Explanations

### L1 human

Drop a marble into a bowl: wherever it starts, it rolls down and comes to rest at the bottom.
The bottom of the bowl is an attractor of the motion.
A swinging pendulum with friction is attracted to the resting position, while a pendulum clock with a driving spring settles into a steady swing, an attracting closed loop.
For the map $x \mapsto x/2$ on the real line, every orbit tends to $0$, so $\set{0}$ is an attractor.