To see it in action, you can go directly to the applet: Fractalina.

The chaos game begins with the selection of a few transformations. These transformations are of a special kind. Each transformation has a center point around which things rotate or compress. We sometimes informally think of the point as being where the transformation lives, so we can say things like "go halfway to the transformation". Each transformation has rotation, compression, and position values that determine how it works.

The chaos game can be explained this way:

- Starting at any point, randomly choose one of the transformations.
- Go part of the way towards the center point of that transformation and rotate part way around it.
- Repeat the process from the resulting point.

The chaos game is a description of the random algorithm for computing the attractor of an Iterated Function System when all the transformation are affine. For more information about the math behind the chaos game, see the section Iterated Function Systems: The Underlying Math.

When a transformation is created it inherits the rotation and compression of the transformation listed directly above it, and gets the position (0,0).

Changing the parameters of a transformation is easy. You can set the value of
any parameter by simply editing the value shown in the appropriate box on the
right of the window. Additionally you can set the position by dragging around
the point in the drawing window. If you drag a point while the system is being
iterated Fractalina will stop iteration, to start again press start. (Note that
on some systems dragging won't register immediately, so start slow. If you *do*
miss the point, Fractalina will think you're trying to zoom, and will display the
zoom rectangle.)

A number of other actions result in the window being cleared. In general, anything that results in the appearance of the fractal changing will cause a clear.

To delete the last point in the list simply press the "Kill Point" button. In the current version only the last point in the list can be deleted, there is no way to delete a point in the middle with out deleting all those below it as well.

To zoom out to your most recent zoom setting, press the "ZoomOut" button. When you are in the un-zoomed state this button won't do anything.

To choose a color mode click on the choice box to the left of "Color selection:" and chose a mode. The default is Random Colors.

The various coloring schemes are a good way to visualize the idea of code space, and understand the address of different regions of the attractor. They also look neat.

Pressing 'r' creates a new point with random color, random rotation, and random compression. This is a neat way to get an idea of the "general fractal". That is, most fractals don't look like the mathematically usual ones, but are much more splotchy (less symmetry). It's also an interesting way to create art.

Pressing 'g' dumps the current image (fractal) to a gif file called frac.gif. Note: this won't work in most applet viewers, for security reasons. The gif dump feature uses the excellent GIFEncoder class by Addam Doppelt.

Pressing 'h' hides or un-hides the transformation settings and points. This is a way for a teacher to challenge students: the teacher sets up the fractal, then hides the settings and asks the students figure them out.

** *Fixed (8/7/96) (I wrote a good work around)***
On

If you find any bugs not listed here, please email the author.

This page was created by Noah
Goodman.

Comments to:
webmaster@geom.umn.edu

Created: Sep 23 1996 ---
Last modified: Tue Oct 8 11:32:24 1996