---
title: "The Chen–Lee Attractor · generative art"
description: "Generation of hyperchaos. Generative art plate #9 by Theodore Vorillas, drawn live in your browser from its equations."
url: "https://vorillaz.com/lab/chen-lee-attractor"
---

![](https://vorillaz.com/_astro/chen-lee-attractor.Db3pcjKX_1UK9h.webp)

fig. #09 · rendered live in your browser from the equations below

# #09 the chen–lee attractor

Generation of hyperchaos.

- date

  2019.05.01

- tags

  generative-art · javascript

- fork

  [codepen ↗](https://codepen.io/TheodoreVorillas/pen/LvKWXe)

The chaotic Chen–Lee system was developed with a formalism based on the Euler equations for the motion of a rigid body. It was proved that this system is the governing set of equations for gyro motion with feedback control. Recently, studies were conducted to explore the dynamic behavior of this system, including fractional order behavior, the generation of hyperchaos and perturbation analysis, control and anti-control of chaos, synchronization, etc.[#1](#ref1)

## The algorithm

```javascript title="chen-lee.js"

const alpha = 5;
const beta = -10;
const delta = -0.38;

const next = (x,y,z) => {
  const dx = alpha * x - y * z;
  const dy = beta * y + x * z;
  const dz = delta * z + (x * y) / 3;
  return {dx,dy,dz};
};
```

## References

- [Alternative implementation of the chaotic Chen–Lee system](https://www.sciencedirect.com/science/article/pii/S0960077908003524)
- [Parametric study of the fractional-order Chen–Lee system](https://www.sciencedirect.com/science/article/pii/S0960077906009295)
- [Controlling chaos and chaotification in the Chen–Lee system by multiple time delays](https://www.sciencedirect.com/science/article/pii/S0960077906010277)
- [Chaos Control and Projective Synchronization of a Chaotic Chen-Lee System](https://www.semanticscholar.org/paper/Chaos-Control-and-Projective-Synchronization-of-a-Li-Li/fbe1a08041ab4e66482f9759102fe0e9fda13d50)