A 7-Fold System for Creating Islamic Geometric Patterns Part 2: Contemporary Expression
Marc Pelletier and Jay Bonner: A 7-Fold System for Creating Islamic Geometric Patterns Part 2: Contemporary Expression. In: Bridges 2012. Pages 149–156
This paper is an abbreviated report on some two decades of research by the authors in the field of 7-fold Islamic geometric patterns. We have expanded the application of this design methodology beyond the historical 7-fold systematic practices identified in Part 1: finding a wide assortment of new polygonal sub-grid elements upon which pattern lines are pre- arranged. What is more, by applying the same basic methodologies used in the 5/10 System, the inherent proportionality of the 7/14 System allows for the creation of 7-fold quasi-crystalline patterns with inflation symmetry, 7-fold non-periodic designs, and 7-fold self-similar designs. This material demonstrates the remarkable flexibility of the 7/14 System of pattern generation, and is intended to open the doors of creative pursuit for others captivated by the beauty of these 7-fold patterns.
1) J. Bonner. Islamic Geometric Pattern: Their Historical Development and Traditional Design Methodology; Springer, 2013 (forthcoming).
2) J. Bonner. Three Traditions of Self-Similarity in Fourteenth and Fifteenth Century Islamic Geometric Ornament; ISAMA-Bridges Conference Proceedings, 2003.
3) M. Senechal. Quasicrystals and Geometry; Cambridge University Press, 1997.
4) P. Steinbach. Golden Fields: A Case for the Heptagon. Mathematics Magazine, Vol. 70, No. 1, Feb. 1997, pp. 22-31. See also: J. Kappraff & G. W. Adamson. A Unified Theory of Proportion; ISAMA-Bridges Conference Proceedings, 2003.
5) E. Makovicky. 800-year old pentagonal tiling from Maragha, Iran, and the new varieties of aperiodic tiling it inspired; Fivefold Symmetry, ed. I. Hargittai, World Scientific, 1992. See also: P. Lu and P. Steinhardt! .......... c&p error
7) E. H. Hankin. The Drawing of Geometric Patterns in Saracenic Art; 1925; Fig. 35. Using many of the same 7/14 sub-grid elements, Nathan Voirol has independently produced a number of remarkable 7-fold self-similar designs in the Persian style. Joe Bartholomew has also working independently with many of these same ornamented modules and has produced a variety of very lovely single-level 7-fold patterns.