Fractal Wallpaper - Symmetry II

Like the Frieze Groups in Symmetry I the Wallpaper Groups are used with fractal patterns in my Wallpaper Machine. The Frieze Groups allow seven different operations to form an endless ornament along one axis, but there are 17 different Wallpaper Groups to fill the Euclidean plane with a basic pattern. In contrast to the Frieze Machine the patterns are not imported as an image but constructed as IFS (watch IFS I - IFS IV).

Figure: Wallpaper Group:
Hide Move Points Group Move Points Iterations:

The source codes are wpkondchaosgame.js and if.js. Thanks to Eric Rowell for the library KineticJS.
Watch the HTML source code of this page, too.

Using the Wallpaper Machine

 Control Elements  Description

First choice element

The fractal pattern (p.e. "Fern")

Second choice element

The Wallpaper Group for the kind of filling the Euclidean plane (p.e. "CMM")

Zoom scroller

A higher zoom factor lets more room for a basic pattern (p.e. "2")

The Iterations edit

A bigger number of iterations increases the images density. You can also use the Draw button again to increase the density.

Move white points

Form the basic pattern

Group Move Points

Move the whole basic pattern with one moved circle

Your task

Move the basic pattern and choose values. Are you able to get a fractal tesselation of the euclidean plane with no overlaps and no big gaps?


Math & Art Gallery


Galerie Cosch


© 2007 Ulrich Schwebinghaus