Fractal Islamic Geometric Patterns Based on Arrangements of n/2 Stars

Aus de_evolutionary_art_org
Wechseln zu: Navigation, Suche


Reference

Phil Webster: Fractal Islamic Geometric Patterns Based on Arrangements of n/2 Stars. In: Bridges 2013. Pages 87–94

DOI

Abstract

Within traditional Islamic geometric design, there is a small but distinct subset of patterns which incorporate no- tions of self-similarity. Such patterns typically use exactly two overlapping levels of self-similarity, with each level comprising similar motifs at two different, related scales. Recently I have constructed a large number of fractal Islamic patterns that pursue a different notion of self-similarity, simultaneously incorporating motifs at multiple— often, infinite—scales within a single pattern. I will first highlight the ways in which these patterns are distinct in nature from related work, both traditional and contemporary. Then, I will explain the details of the technique I have devised for using arrangements of {n/2} stars as a basis for discovering and constructing a wide variety of new fractal Islamic patterns.

Extended Abstract

Bibtex

Used References

[1] Bartholomew, J. “Girih Extended”. http://www.joebartholomew.com/girih139.html (as of Jan-uary, 2013)

[2] Bonner, J. “Three Traditions of Self-Similarity in Fourteenth and Fifteenth Century Islamic Geometric Ornament”, Bridges Conference Proceedings (2003).

[3] Bonner, J. Islamic Geometric Patterns: Their Historical Development and Traditional Design Method- ology, Springer, 2013 (forthcoming).

[4] Bonner, J. Personal communication, January 2013.

[5] Bonner, J. and Pelletier, M. “A 7-Fold System for Creating Islamic Geometric Patterns Part 1: Historical Antecedents”, Bridges Conference Proceedings (2012).

[6] Castera, J. “Play with Infinity”, Bridges Conference Proceedings (2003).

[7] Dunham, D. “Hyperbolic Islamic Patterns A Beginning”, Bridges Conference Proceedings (2001).

[8] Fathauer, R. “Fractal tilings based on kite- and dart-shaped prototiles”, Computers & Graphics, 25:323- 331, 2001.

[9] Fathauer, R. “Compendium of Fractal Tilings”. http://www.mathartfun.com/shopsite_sc/store/html/Compendium/encyclopedia.html (as of January, 2013)

[10] Fathauer, R. Personal communication, January 2013.

[11] Gr ̈unbaum, B. and Shephard, G. C. Tilings and Patterns, W. H. Freeman, 1987.

[12] Kaplan, C. and Salesin, D. “Islamic Star Patterns in Absolute Geometry”, ACM Transactions on Graph- ics, 23(2):97-119, April 2004.

[13] Lee, A. “Islamic Star Patterns”, Muqarnas 4, 182-197, 1987.

[14] Lu, P. and Steinhardt, P. “Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture”, Science, 315:1106, 2007.

[15] Pelletier, M. and Bonner, J. “A 7-Fold System for Creating Islamic Geometric Patterns Part 2: Contem- porary Expression”, Bridges Conference Proceedings (2012).


Links

Full Text

http://archive.bridgesmathart.org/2013/bridges2013-87.pdf

intern file

Sonstige Links

http://archive.bridgesmathart.org/2013/bridges2013-87.html