---
title: "The Rössler Attractor · generative art"
description: "Stretch, fold, repeat. Generative art plate #17 by Theodore Vorillas, drawn live in your browser from its equations."
url: "https://vorillaz.com/lab/rossler-attractor"
---

![](https://vorillaz.com/_astro/rossler-attractor.CL2YcsXP_D4TEr.webp)

fig. #17 · rendered live in your browser from the equations below

# #17 the rössler attractor

Stretch, fold, repeat.

- date

  2026.09.14

- tags

  generative-art · javascript

In 1976 Otto Rössler set out to find the simplest possible system of equations that could still behave chaotically. The result has a single nonlinear term, `z * x`, and yet it produces a strange attractor. [#1](#ref1)

The Rössler attractor is a great way to _see_ how chaos works. Trajectories spiral outwards on a flat disc, and once they drift far enough from the centre they get lifted up, folded over and dropped back near the middle. That stretch-and-fold motion, repeated forever, is the mechanism behind most chaotic systems, and here it is visible in a single band.

## The algorithm

```javascript title="rossler-attractor.js"
const a = 0.2;
const b = 0.2;
const c = 5.7;

const next = (x,y,z) => {
  const dx = -y - z;
  const dy = x + a * y;
  const dz = b + z * (x - c);
  return {dx,dy,dz};
};
```

Try lowering `c` towards `4`: the attractor settles into a periodic orbit, then doubles its period again and again as `c` grows, until it falls into chaos.

## References

- [An equation for continuous chaos](https://doi.org/10.1016/0375-9601\(76\)90101-8), Physics Letters A, 57(5), 1976.
- [Rössler attractor](https://en.wikipedia.org/wiki/R%C3%B6ssler_attractor)