The Chaos game is a simple iterative way to create fractals. The only thing we need to keep track of is a single point; at each iteration it is moved towards a randomly chosen vertex. You can find a more detailed description at the bottom of this page, as well as a small gallery.

Meanwhile, can you create your own unique fractal?

Be cautious with the number of samples; the image is rendered in your browser. Feel free to send me your creation!

Number of vertices: 4

Number of samples: 100000

Jumping ratio: 0.50

Rule: None

Filter: Sporadic inspiration

Filter strength: 0.9

Filter size: 1.0

Fan-art

Magnificent fractals made by Lukas:

Gerda’s astounding dotty fractals:

Description of the process

The process follows the following steps:

  • Start with a point within the n-gon (e.g. the centre).
  • Choose a rule. Examples of rules can be: “Don’t ever jump towards the same vertex twice in a row”, or, “Don’t jump towards any neighbouring vertex of the vertex to which you jumped last”.
  • Choose a filter. This is a small area in the centre of the n-gon; we will prevent our point to land in the area during the process.
  • Repeat multiple times (This is controlled by Number of samples slider) the next steps:
    • Keep choosing a vertex at random, until it is compliant with your rule.
    • Jump the fraction of the way towards this vertex (This is the jumping ration).
    • With probability filter strength, check if the point lands in the area of the filter. If it is the case, we skip this iteration altogether.

There is also a small article on »wikipedia« worth checking out.