page 7


Colored version:

[1] The set of tiles with C-curves and an examination of tilings that can be made with them is presented in Spiral Tilings with C-curves by Chris K. Palmer, Bridges Proceedings 2005.
[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. Pages 65-9 describe K-uniform tilings.
[4] Recursive methods developed by the author from 1997 to the present show that an infinite variety of spiral tilings can be composed. These will be presented in forthcoming papers. The principles presented in this paper apply for tilings on spheres can be found here: Hyperbolic tilings can also be composed with these tiles and the addition of other even sided tiles.
[5] Colored versions of Figures 7-11 and other compositions can be found here: A program to explore some elementary compositions of the tiles shown in Figure 7-8 can be seen here: