The 7 Curve, Carpets, Quilts, and Other Asymmetric, Square-Filling, Threaded Tile Designs
Inhaltsverzeichnis
Reference
Douglas McKenna: The 7 Curve, Carpets, Quilts, and Other Asymmetric, Square-Filling, Threaded Tile Designs. In: Bridges 2007. Pages 225–232
DOI
Abstract
Visually intriguing tiling patterns arise from an asymmetric “threading” technique for constructing space-filling curves in the square. The method uses four square tiles in varying or uniform sizes, each the mirror or negative image of a single directed line segment. On varying size “quilt” dissections, the simplest pattern, built of just seven threaded tiles, is as fundamental a construction as the classic Peano or Hilbert Curves. For uniform n × n tilings, a computer enumeration finds 0, 0, 0, 6, 5, 366, 0, 4110384, . . . of these special threaded tile designs for 1 ≤ n ≤ 8. The combinatoric explosion of possible patterns permits one to pick and choose among them using æsthetic criteria.
Extended Abstract
Bibtex
Used References
[1] Golomb, S., “Replicating figures in the plane”, Math. Gazette, Vol. XLVIII, No. 366 (1964).
[2] Sagan, H., Space-Filling Curves, Springer-Verlag (1994), ch. 1–3.
[3] McKenna, D. M., “Asymmetry vs. symmetry in a new class of space-filling curves”, Conf. Proc. Bridges Math. Connections in Art, Music, and Science (2006), 371–378.
[4] Sloane, N. A. J., Handbook of Integer Sequences. Academic Press, NY (1973).
[5] Conway, J. H. “Mrs. Perkins’s Quilt.”, Proc. Camb. Phil. Soc. 60 (1964), 363–368.
[6] Mandelbrot, B. B., The Fractal Geometry of Nature (1982), 144.
Links
Full Text
http://archive.bridgesmathart.org/2007/bridges2007-225.pdf
