Don’t worry, this is one academic, Associate Professor Craig S Kaplan, who knows how to bridge the gap between traditional Islamic art and computer science and technology whilst still making it an interesting lecture!
There are examples towards the end of how these patterns have been applied to various materials and structures using technological and digital methods.
Geometric Design for Beginners is a series of tutorials available on Tuts+ providing instructions for producing your own geometric patterns. Posted by Joumana Medlej, these are step by step instructions designed for beginners but continue on to more complex patterns. Easy to follow and a convenient resource for working at your own pace. Read more here: Geometric Design for Beginners
I’ve just come across the Tradigital website (an Arabic publishing studio associated with the Thesauraus Islamicus Foundation and Islamic Art Network) where I have found a very helpful animation of how one Qur’anic illumination pattern is constructed. The design is based on 6-fold geometry from which a 12-pointed star pattern is produced.