https://github.com/ubavic/chaos-game

Interactive demonstration of the Chaos game
https://github.com/ubavic/chaos-game

complex-dynamics fractals iterated-function-system

Last synced: about 1 year ago
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Interactive demonstration of the Chaos game

• Host: GitHub
• URL: https://github.com/ubavic/chaos-game
• Owner: ubavic
• License: mit
• Created: 2023-03-17T23:22:22.000Z (about 3 years ago)
• Default Branch: main
• Last Pushed: 2023-03-26T17:33:12.000Z (about 3 years ago)
• Last Synced: 2025-03-14T21:46:29.640Z (over 1 year ago)
• Topics: complex-dynamics, fractals, iterated-function-system
• Language: JavaScript
• Homepage: https://ubavic.rs/chaos_game
• Size: 122 KB
• Stars: 1
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

          
# Chaos game

Interactive demonstration of the [Chaos game](https://en.wikipedia.org/wiki/Chaos_game), written in pure JavaScript. This program renders images to a canvas element, while commands are implemented via HTML form elements and SVG.

In this demonstration, all vertices and parameters are treated as complex numbers.

The orbit of the point $P_0$ is generated iteratively by the formula

$$P_{i+1} = \lambda (P_i + V)$$

where $V$ is a randomly chosen vertex of the polygon, and $\lambda$ is fixed parameter (in  the "original" Chaos game, $\lambda = \frac{1}{2}$).

![Chaos game](./chaos.png)

## Hacking and Contributing 

Even if the code contains a few hundred lines, the main drawing logic is concentrated in a few lines of the `draw` function.

All other functions are used for UI.

Some ideas for future development

 + Better control of 'clearing' between redraws

 + More control of the number of iterations per frame. Automatic selection based on the time required to render a frame

 + Advanced rules: disallowing consequent selection of same vertex, forbidden domains, etc...

 + Switching to WebGL renderer/WASM core if that brings more performance

Contributions and new ideas are more than welcome.