‘What if there was no repetition’ generated a really great discussion, well worth a read through the comments. Here are some contributions which came out of this discussion, starting with some work created by David Riley: Recursive Jitter and Recursive. David has been brushing up on his creative programming. If you click on Recursive Jitter it will take you to the active programme, the image here is just a snapshot. Recursive is a simple example of recursive programming code. You can see more of David’s work on his website, CODED IMAGES.
In addition, LOLFACEMCTHISONE shared the fascinating world of quasicrystal structure. Not only are their physics different to other crystal structure, and are non-repeating structures, but medieval Islamic art was producing these forms in mosaics such as the Girih tiles 500 years before they were discovered in the West. Here are some images from google of these structures: