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Special Topics:Tilings

Arbitrary substitution tiling by Chaim Goodman-Strauss

  
All these squares are congruent. Yes, its true, by tautology, because we can define our space of congruences ourselves. This is a substitution tiling, using these weird congruences. Amazingly, there are matching rules on these tiles, in this strange space, so that ANY tiling with these tiles satisfying the matching rules looks basically like this.

How to make it: MacPaint, of all things.

Image created: January 1995

[Arbitrary substitution tiling]

Copyright © January 1995 by The Geometry Center, Univerity of Minnesota. All rights reserved.
For permission to use this image, contact permission@geom.umn.edu.

External viewing: small (100x100 7k gif), medium (500x693 185k gif), or original size (468x648 888k tiff).

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Created: Sat May 22 23:17:51 CDT 1999 --- Last modified: Sat May 22 23:17:51 CDT 1999