---
title: "The Halvorsen Attractor · generative art"
description: "Deterministic Chaos. Generative art plate #11 by Theodore Vorillas, drawn live in your browser from its equations."
url: "https://vorillaz.com/lab/halvorsen-attractor"
---

![](https://vorillaz.com/_astro/halvorsen-attractor.B4rmTxr5_Z2eCRAI.webp)

fig. #11 · rendered live in your browser from the equations below

# #11 the halvorsen attractor

Deterministic Chaos.

- date

  2019.05.04

- tags

  generative-art · javascript

- fork

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

The Halvorsen’s cyclically symmetric attractor can produce interesting artistic results using a single entry parameter.

For this visualization, I have decided to use a different coloring palette, as well as creating a projection effect using a diffused particle system.

## The algorithm

```javascript title="halvorsen-attractor.js"

const a = 1.4;

const next = (x,y,z) => {
  const dx = -a * x - 4 * y - 4 * z - y * y;
  const dy = -a * y - 4 * z - 4 * x - z * z;
  const dz = -a * z - 4 * x - 4 * y - x * x;
  return {dx,dy,dz};
};
```

## References

- [Elegant Chaos: Algebraically Simple Chaotic Flows](https://www.researchgate.net/publication/268721148_Elegant_chaos_Algebraically_simple_chaotic_flows_Dedicated_to_the_memory_of_Edward_Norton_Lorenz)
- [Advances in Chaos Theory and Intelligent Control](http://www.gbv.de/dms/tib-ub-hannover/866444076.pdf)
- [Novel quantification for chaotic dynamical systems with large state attractors](http://www.wseas.us/e-library/conferences/2011/Angers/ACMMA/ACMMA-17.pdf)
- [Deterministic Chaos](http://dataanalysis.vsb.cz/data/Vyuka/NAVY/Deterministic%20Chaos.pdf)