Some tilings

These were done either for a math class I offered at Williams College, or as a part of my generalized research (vaguely applied to metallurgy and computer architecture) sporadically conducted over the past few decades. There are more, if I ever have time to put them here.

A nifty little triangle that once configured into a pentagon, tiles aperiodically.

 

 leafpat2A rather nice pattern based on a pentagon employing slightly unusual (for tiles) angles. The link shows another use.

 

 

The simple 60 degree rhombus makes for some pretty patterns.

 

More with rhombi

Three triangles together

  Pseudo-regular pentagon

Dancing pentatiles with obligatory and optional determinism

A demonstration that this pentatile tiles the plane nondeterministically (or "nonperiodically").

Half-hexagons -- are all tilings with this tile dominable (coverable by dominos)? Triangles and dominos -- Tilings by this triangular tile
are not always coverable by dominos.

This little applet displays a sort of random walk using a triangular tile.

Look here for a sample of my ongoing research.


See copyright notice.