---
title: "The Thomas Attractor · generative art"
description: "Deterministic Labyrinth Chaos. Generative art plate #8 by Theodore Vorillas, drawn live in your browser from its equations."
url: "https://vorillaz.com/lab/thomas-attractor"
---

![](https://vorillaz.com/_astro/thomas-attractor.V9LIuTCA_Etyng.webp)

fig. #08 · rendered live in your browser from the equations below

# #08 the thomas attractor

Deterministic Labyrinth Chaos.

- date

  2019.04.22

- tags

  generative-art · javascript

- fork

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

In the dynamical systems theory, Thomas’ cyclically symmetric attractor is a 3D strange attractor originally proposed by René Thomas. It has a simple form which is cyclically symmetric in the x,y, and z variables and can be viewed as the trajectory of a frictionally dampened particle moving in a 3D lattice of forces. The simple form has made it a popular example.

## The algorithm

```javascript title="thomas-attractor.js"
const b = 0.19;

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

## References

- [Thomas’ cyclically symmetric attractor](https://en.wikipedia.org/wiki/Thomas%27_cyclically_symmetric_attractor)
- [Deterministic chaos seen in terms of feedback circuits: Analysis, synthesis, ‘labyrinth chaos’](https://www.worldscientific.com/doi/abs/10.1142/S0218127499001383)
- [Labyrinth Chaos](https://www.worldscientific.com/doi/abs/10.1142/S0218127407018245)