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.
A 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
Dancing pentatiles with obligatory and optional determinism
A demonstration that this pentatile tiles the plane nondeterministically (or "nonperiodically").
-- 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.
for a sample of my ongoing research.
See copyright notice.