Sadun, L.
Some Generalizations of the Pinwheel Tiling
(357K, Postscript)

ABSTRACT.  We introduce a new family of nonperiodic tilings, based on 
a substitution rule that generalizes the pinwheel tiling 
of Conway and Radin.  In each tiling the tiles are similar 
to a single triangular prototile.  In a countable
number of cases, the tiles appear in a finite number of sizes and 
an infinite number of orientations.  These tilings generally do not
meet full-edge to full-edge, but {\it can} be forced through local 
matching rules.  In a countable number of cases, the tiles appear 
in a finite number of orientations but an infinite number of sizes, 
all within a set range, while in an uncountable number of cases both 
the number of sizes and the number of orientations is infinite.