The Chaos Game
See the commentary for W 2000 and W 2002
for a description of how to draw fractals using the Chaos Game.
These images weree made with the Chaos Game applet.
Compare these images with those made by an IFS; see the IFS page.
See also the Chaos Game Variation page for examples of images drawn with
unusual probabilities.
The Sierpinski Triangle. Number of points: 50 100, 200, 500, 1000, and final image
The Cantor Maze. Number of points: 50 100, 200, 500, 1000, and final image
The Fern. Number of points: 50 100, 200, 500, 1000, and final image
A fractal tree. Number of points: 50 100, 200, 500, 1000, and final image
Here's an object that was drawn with the chaos game, but is not a fractal (it is not exactly self-similar).
To draw this, the Sierpinski
IFS was used. The sequence { s1, s2, s3, . . . } that was used in the game was
constructed by first generating a random sequence of 1' s, 2' s and
3' s with equal probabilities, and then removing all occurences of the string 12 from
the sequence (which imples that no region with address that contains the string 21 is present in the image).
This image was drawn with the Modified Chaos Game applet (written by Danny Heap).
