For the time being I gladly leave the last word to [url=http://www.bonner-design.com/]Jay Bonner[/url].[br]In 2017 he published Islamic Geometric Patterns, a 500 pages book you can call the reference book on the subject. Bonner offers a very elaborated classification of patterns. Don’t expect an easy readable book of nice photographs. Literally and figuratively it’s pretty tough but excellently informed. The introduction is written by no other than George Penrose himself.

Bonner agrees with what he calls the 'polygonal technique', already described by Hankin in 1925 als PIC (polygons in contact). According to Bonner it’s the most important and mostly technique by the muslim artists. As others Bonner constats there’s surprising little historical illustrative material on the subject. Although he agrees there’s more than one possible theory he proposes the polygonal thechnique as the most relevant for the immense diversity and complexity. It’s documented in the famous Topkapi scrol land easy to use for all kinds of patterns, which is not the case for all other proposed techniques like the point-joining method. This technique starts from a unit repeat in which lines and circles create a pattern. According to Bonner this technique has got three big disadvantages: [br]1 It isn’t suitable to create original new patterns, but just to a stepwise repeat of one pattern; [br]2 It’s unpractical to create complexe patterns with more than one center of symmetry; [br]3 the different steps of every pattern have to be memorised or documented separately and[br] for this there’s no historical base as there is for the polygonal method. [br]But Bonner is critical to the thesis of quasi-periodicity posed by Lu en Steinhardt. Thes auteurs emphasise that, while commenting their properties you mustn’t isolate the pattern in their limited area. Bur according to Bonner that’s exactly what Lu en Steinhardt in their comments on the Isfahan patterns since the indeed remarkable pattern fits into a regular, bigger and well-known pattern of decagons and bow ties.

Who else than Roger Penrose could Bonner ask to write the foreword for his book after all the fuzz and comments on quasi-periodicity and Penrose tilings? Penrose writes Islamic patterns, although being abstract and geometrical, radiate a natural beauty but as well testify a sharp and subtitle understanding and skill in the use of geometrical figures. On the question of quasi-periodicity he tends to agree with Bonner since there a general search for symmetry in them.