Start with the two basic Penrose "prototiles"
and think of them as belonging to
generation-zero of a sequence of higher generation "supertiles".
The construction of
these "supertiles" now begins. The A-supertile
of generation-1 uses two generation
-zero A-tiles and one generation-zero B-tile, cut in half
as necessary. The B-supertile
of generation-1 uses one generation-zero A-tile and one
generation-zero B-tile.
The remarkable feature about the supertiles is that the
new bands enforce exactly
the same matching possibilities as the original
generation-zero tiles. You can think of
them as "prototiles" with different but
equivalent markings. This means that the same
cut-and-paste procedure can be applied to the generation-1
supertiles to create
generation-2 supertiles, and on and on forever. Click,
below, to see the generation-2
supertiles.
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