Adapter Tiles Evolves the Girih Tile Set

This is a video for the presentation of my paper for the Bridges Conference.
Chapters:
00:00 Adapter Tiles Evolves the Girih Tile Set
04:02 Non-Equilaterality
06:07 Adapters
10:15 The Evolved Tile Set
12:41 Summary and Conclusions
14:14 Acknowledgement

The paper is the first of many papers I have in the pipe line. The first five covers non-equilaterality, and this paper set the stage for the rest.

Update: I have to apologize for missing out on a key paper that I should have mentioned: "Hybrid 1-point and 2-point Constructions for some Islamic Geometric Designs" from 2010 by Peter R. Cromwell.
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Abstract
This document presents an evolved Girih tile set beyond the five Girih Tiles popularized by Lu and Steinhardt. Additional tiles have been presented in multiple papers before, but here, a wider set is officially defined. I refer to this as the evolved tile set or evolved Girih tile set.

It includes the adapter tiles, which also have been presented before, but not defined as a group or part of a tile set. Adapter tiles differ from the five Girih Tiles as the latter only have equilateral sides. This paper presents one category of adapters containing tiles having at least one side with the length of Φ .

The aim is to establish non-equilateral sides as a necessary concept to enable tiling of a greater number of existing Islamic geometric patterns. This opens up for future introductions of other categories of non-equilateral tiles.
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References
[1] J. Bonner. “Three traditions of self-similarity in fourteenth and fifteenth century Islamic geometric ornament.” ISAMA-Bridges Proceedings, Alhambra, Spain, 2003, pp.1–12.
http://archive.bridgesmathart.org/200....

[2] J. Bonner. Islamic Geometric Pattern. Springer-Verlag, 2017. https://www.springer.com/gp/book/9781....

[3] J. Bourgoin. Les Eléments de l’Art Arabe: Le Trait des Entrelacs. Firmin-Didot. 1879. Plates reprinted in Arabic Geometric Pattern and Design. Dover Publications, 1973. https://archive.org/details/LesElemen....

[4] J-M. Castera. “Persian Variations.” Nexus Network Journal, vol. 18, no. 1, 2016.. https://www.nexusjournal.com/volume-1....

[5] P. R. Cromwell. “Islamic Geometric Designs from the Topkapı Scroll II: A Modular Design System”. Journal of Mathematics and the Arts, vol. 4, no. 3, 2010, pp. 119–136. https://doi.org/10.1080/1751347090331....

[6] Girih Tiles. https://en.wikipedia.org/wiki/Girih_t....

[7] E. H. Hankin. “The Drawing of Geometric Patterns in Saracenic Art”. Memoires of the Archaeological Survey of India. Vol 15. Government of India Central Publication Branch, 1925.

[8] J. Kepler. Harmonice Mundi, CreateSpace Independent Publishing Platform, 2014.

[9] P.J. Lu and P.J. Steinhardt. “Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture”. Science, Vol. 315, Issue 5815, 2007, pp. 1106–1110. https://science.sciencemag.org/conten...

[10] G. Necipoğlu. The Topkapı Scroll: Geometry and Ornament in Islamic Architecture. Getty Center Publication, 1995.

[11] Penrose Tiling. https://en.wikipedia.org/wiki/Penrose....