# #11 - The Halvorsen Attractor

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The Halvorsenâ€™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

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
- Advances in Chaos Theory and Intelligent Control
- Novel quantification for chaotic dynamical systems with large state attractors
- Deterministic Chaos