Unexpected Beauty Hidden in Radin-Conway's Pinwheel Tiling

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Douglas G. Burkholder: Unexpected Beauty Hidden in Radin-Conway's Pinwheel Tiling. In: Bridges 2015. Pages 383–386



In 1994, John Conway and Charles Radin created a non-periodic Pinwheel Tiling of the plane using only 1 by 2 right triangles. By selectively painting either every fifth triangle or two out of every five triangles, based only upon their location in the next larger triangle, one can discern 15 unexpected and distinctive patterns. Each of these patterns retains the non-periodic nature of the original tiling.

Extended Abstract


 author      = {Douglas G. Burkholder},
 title       = {Unexpected Beauty Hidden in Radin-Conway's Pinwheel Tiling},
 pages       = {383--386},
 booktitle   = {Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture},
 year        = {2015},
 editor      = {Kelly Delp, Craig S. Kaplan, Douglas McKenna and Reza Sarhangi},
 isbn        = {978-1-938664-15-1},
 issn        = {1099-6702},
 publisher   = {Tessellations Publishing},
 address     = {Phoenix, Arizona},
 note        = {Available online at \url{http://archive.bridgesmathart.org/2015/bridges2015-383.html }},
 url         = {http://de.evo-art.org/index.php?title=Unexpected_Beauty_Hidden_in_Radin-Conway's_Pinwheel_Tiling },

Used References

Charles Radin, The Pinwheel Tilings of the Plane, Annals of Mathematics, Vol. 139, 1994, pp. 661-702.


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