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I stumbled across this interesting article.  What do you call something that is infinitely complex but not self-similar?  I like the name 'anti-fractal', but would 'chaotic' suffice?  Does chaos imply lack of order?  These patterns are completely mathematically ordered...

http://www.reuters.com/article/scienceNews/idUSN2245118920070222?src=022207_1643_ARTICLE_PROMO_also_on_reuters&pageNumber=1

Medieval Muslims made stunning math breakthrough



WASHINGTON (Reuters) - Magnificently sophisticated geometric patterns in medieval Islamic architecture indicate their designers achieved a mathematical breakthrough 500 years earlier than Western scholars, scientists said on Thursday.

By the 15th century, decorative tile patterns on these masterpieces of Islamic architecture reached such complexity that a small number boasted what seem to be "quasicrystalline" designs, Harvard University's Peter Lu and Princeton University's Paul Steinhardt wrote in the journal Science.

Only in the 1970s did British mathematician and cosmologist Roger Penrose become the first to describe these geometric designs in the West. Quasicrystalline patterns comprise a set of interlocking units whose pattern never repeats, even when extended infinitely in all directions, and possess a special form of symmetry.

Excellent thanks for the link.  Although it is repeating (tiling) the pattern.  Would be nice to see a non-repeating version of this program.