Self-similar Tilings Based on Prototiles Constructed from Segments of Regular Polygons

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Reference

Robert W. Fathauer: Self-similar Tilings Based on Prototiles Constructed from Segments of Regular Polygons. In: Bridges 2000. Pages 285–292

DOI

Abstract

Two infinite families of self-similar tilings are described which have apparently not been reported before. Each tiling is based on a single prototile that is a segment of a regular polygon. Each tiling is also edge to edge and bounded in the Euclidean plane, by means of the tiles being reduced in size. by a fixed scaling factor. This results in self similarity. Tilings are constructed from these prototiles that are of a rich visual complexity, and an example is· given of an Escher-like design based on one of these tHings.

Extended Abstract

Bibtex

Used References

[1] The Magic Mirror of M.C. Escher. by Bruno Ernst (Ballantine Books. New York, 1976).

[2] RobertW. Fathauer. Extending Recognizable-motif Tilings to Multiple-solution Tilings and Fractal Motifs. to be published in the Proceedings of the Centennial Escher Congress. held in Rome and Ravello in June of 1998.

[3] Peter Raedschelders. private communication. Examples can be seen on Mr. Raedschelders web site. http://home.planetinternet.be/-praedschlindex.htm.

[4] Chaim Goodman-Strauss. private communication. Prof. Goodman-Strauss has constructed a number of tilings in which each tile is a fractal object related to the Koch snowflake.

[5] Robert W. Fathauer. presented at the 1999 Bridges Conference (Winfield. Kansas. August 1999).


Links

Full Text

http://archive.bridgesmathart.org/2000/bridges2000-285.pdf

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http://archive.bridgesmathart.org/2000/bridges2000-285.html