Simple Rules for Incorporating Design Art into Penrose and Fractal Tiles
Inhaltsverzeichnis
Reference
San Le: Simple Rules for Incorporating Design Art into Penrose and Fractal Tiles. In: Bridges 2012. Pages 259–266
DOI
Abstract
Incorporating designs into the tiles that form tessellations presents an interesting challenge for artists. Creating a viable M.C. Escher-like image that works esthetically as well as functionally requires resolving incongruencies at a tile’s edge while constrained by its shape. Escher was the most well known practitioner in this style of mathematical visualization, but there are significant mathematical objects to which he never applied his artistry including Penrose Tilings and fractals. In this paper, we show that the rules of creating a traditional tile extend to these objects as well. To illustrate the versatility of tiling art, images were created with multiple figures and negative space leading to patterns distinct from the work of others. 1
Extended Abstract
Bibtex
Used References
[1] B. M. Adcock, K. C. Jones, C. A. Reiter, and L. M. Vislocky. Iterated function systems with symmetry in the hyperbolic plane. Comp.& Graph., pages 791–796, 2000.
[2] D. Bailey. David bailey’s world of escher-like tessellations. http://www.tess-elation.co.uk/penrose-tilings/thin-and-thick-rhombi, 2009.
[3] R. Bandt and P. Gummelt. Fractal penrose tilings i. construction and matching rules. Aequ. math., 53:295–307, 1997.
[4] R. A. Dunlap. Fivefold symmetry in the graphic art of m.c. escher. Fivefold Symmetry, 1994.
[5] B. Ernst. The Magic Mirror of M. C. Escher. 1995.
[6] R. Fathauer. Tree of knowledge. http://mathartfun.com/shopsite sc/store/html/Art/Tree0Knowledge.html, 2002.
[7] R. Fathauer. Extending escher’s recognizable-motif tilngs to multiple-solution tilings and fractal tilings. M.C. Escher’s Legacy: A Centennial Celebration, pages 154–165, 2005.
[8] R. Fathauer. Fractal Trees. 2011.
[9] M. James. The Second Quiltmaker’s Handbook: Creative Approaches to Contemporary Quilt Design. 1996.
[10] C. S. Kaplan and D. H. Salesin. Dihedral escherization. GI ’04 Proc. Conf. Graphics Interface 2004, pages 255–262, 2004.
[11] S. Le. The art of space filling in penrose tilings and fractals. http://arxiv.org/abs/1106.2750, 2010.
[12] E. A. Lord. Quasicrystals and penrose patterns. Current Sci., pages 313–319, 1991.
[13] N. Mirzoeff. Bodyscape: Art, Modernity and the Ideal Figure. 1995.
[14] J. Osborn. ozbird.net penrose gallery. http://www.ozbird.net/PG.html, 2001.
[15] P. Raedschelders. Tilings and other unusual escher-related prints. M.C. Escher’s Legacy: A Centennial Celebration, pages 230–243, 2005.
[16] D Schattschneider and M. Emmer. M.C. Escher’s Legacy: A Centennial Celebration. 2005.
Links
Full Text
http://archive.bridgesmathart.org/2012/bridges2012-259.pdf
