I have documented my research and theories in a recently published book: Islamic Geometric Patterns: their Historical Development and Traditional Methods of Derivation. This is published by Springer. My book contributes to the study of this design discipline in three primary ways: Chapter 1 chronicles the historical development of this art form; Chapter 2 is concerned with the design diversity and geometric characteristics found within this tradition; and Chapter 3 is a highly detailed exposition of the design methodology associated with the polygonal technique. The final chapter is contributed by Craig Kaplan and concerns the use of mathematical algorithms to generate patterns with computers. This book has over 600 pages, with 105 photographs and over 540 detailed illustrations. The forward is by Sir Roger Penrose.
http://www.springer.com/us/book/9781441902160
In addition to my recently published book, prior peer reviewed publications on this subject include:
The Historical Significance of the Geometric Designs in the Northeast Dome Chamber of the Friday Mosque at Isfahan. Published in the Nexus Networks Journal, Springer (April 2016, Volume 18, issue 1, pp. 55-103).
https://link.springer.com/article/10.1007/s00004-015-0275-3
Please note: with apologies, this link is to the Springer Link sales website, and only the abstract and references are available without payment.
A 7-Fold System for Creating Islamic Geometric Patterns, Part 1: Historical Antecedents (pp. 141-148), and Part 2: Contemporary Expression (pp. 149-156). Co-authored with Marc Pelletier. Published in the Bridges Conference proceedings, 2012.
http://archive.bridgesmathart.org/2012/bridges2012-141.html
http://archive.bridgesmathart.org/2012/bridges2012-149.html
Three Traditions of Self-Similarity in Fourteenth and Fifteenth Century Islamic Geometric Ornament. Published in the ISAMA/Bridges Conference Proceedings, 2003.
http://archive.bridgesmathart.org/2003/bridges2003-1.html
Note: Other publications are contributions to various books on Islamic art and geometric design. Please see my complete C.V. for details.
The following is a link to a podcast of an interview with Lynn Cline, the host of Cline’s Corner on KSFR, a Santa Fe radio station, in which I speak about my work with Islamic geometric design and ornament:
The following is a link to an article about me in the Pasatiempo magazine from Friday, September 29, 2017. This is the arts magazine that is published each Friday in the New Mexican newspaper: