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Thursday, March 25, 2010
First Aperiodic Tiling With A Single Shape
Mathematicians discover how to tile a plane in a nonrepeating pattern using a single shape.
Today, Joshua Socolar and Joan Taylor at Duke University announce that they have solved the einstein problem and in the process they've discovered an entirely new way to approach the problem.
"The tile presented here is the only known example of an aperiodic tile," they say.
Almost the 3d monotile...
Socolar and Taylor's Aperiodic monotile
Patch of tiling, the red lines show a little of the structure of the tiling. The single grey tile shows how the different pieces of the tile fit together with its neighbours.
Patch of tiling with the 3d monotile. Note how the tiles fit together at different levels.
clipped from www.tilings.org.uk
clipped from www.technologyreview.com
clipped from maxwelldemon.com
