Spiral Tilings with C-curves Using Combinatorics to Augment Tradition

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Chris K. Palmer: Spiral Tilings with C-curves Using Combinatorics to Augment Tradition. In: Bridges 2005. Pages 37–46



Spiral tilings used by artisans through the ages using C-curves are identified. The complete combinatoric set of these tiles is determined and tilings that can be made with them are examined.

Extended Abstract


Used References

[1] The complete set of tiles that includes S-curves, C-curves and combinations of S-curves and C-curves, a study of those compositions used by traditional artisans and many that augment tradition utilizing them is presented in Scurls and Whirl Spools by Chris K. Palmer, VisMath Volume 10.

[2] Some interesting examples of traditional compositions that use tilings with irregular underlying tilings not addressed by this paper can be seen in Celtic Art the methods of Construction, George Bain, Dover ISBN 0-486-22923-8, page 66 plates 11-12. Pages 64-65 Plates 7-10 contain examples of frieze patterns and rosettes utilizings spirals also not addressed in this paper.

[3] After the famous crytallographer Fritz Laves. See Tilings and Patterns, Grunbaum and Shepard, ISBN 0-7167-1193-1, pages 95-98

[4] Recursive methods developed by the author from 1997 to the present show that within the restrictions imposed by the rules described in this paper an infinite variety of spiral tilings can be composed. These will be presented in forthcoming papers and as part of a doctoral thesis. The principles presented in this paper apply for tilings on spheres: http://www.shadowfolds.com/websphere/wspools.htm. Hyperbolic tilings can also be composed with these tiles and the addition of other even sided tiles.


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