Socolar and Taylor’s Aperiodic Tiling With A Single Shape

clipped from www.tilings.org.uk

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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.
clipped from maxwelldemon.com
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.
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  1. How do Shapes Fill Space?
  2. Technology Review: Blogs: arXiv blog: First Aperiodic Tiling With A Single Shape
  3. Socolar and Taylor’s aperiodic tile. « Maxwell’s Demon
  1. Make: Online : World's first aperiodic tiling with a single shape
  2. Make: Online : Socolar-Taylor aperiodic tile models on Thingiverse
  3. Aperiodic tiling - Wikipedia, the free encyclopedia
  4. [1003.4279] An aperiodic hexagonal tile
  5. Edmund Harriss
  6. A-single-tile | Products & Tech News
  7. Socolar-Taylor Aperiodic Tile by Gelada - Thingiverse
  8. First Aperiodic Tiling With A Single Shape | www.onu.ro