Inspiration was taken from Islamic Patterns: An Analytical and Cosmological Approach and all images are created using geometric algorithms -- no images or screenshots.
The patterns properties can be modified, the patterns aren't static.
Having downloaded and installed Cappuccino, to build this:
git clone git://github.com/gorenje/capp_patterns.git git submodule update --init cd Libraries/Cappuccino jake release && jake debug cd ../GRKit jake release && jake debug cd ../.. open index.html
Cappuccino is linked into this project in the Libraries directory and will be used from there. That makes sure that a working version of Cappuccino is being used ;)
GRKit is just a bunch of helpers for doing rotation and geometry calculations.
You can view patterns but also edit thier properties by using the 'Pattern Property' button on the top left. The current settings can be dumped to the console window (i.e. FireBug or Web Inspector) but can only be integrated by cloning the project and adding a new pattern class.
To demostrate (to myself) how to draw in Cappuccino and to understand how to generate complex patterns just using circles. But basically, it's the same kind of 'why' as in 'why did hillary climb that mountain'.