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Math Forum » Discussions » Inactive » geometry.forum

Topic: Penrose and Quasiperiodic Tilings
Replies: 18   Last Post: Apr 1, 1998 11:52 AM

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Heidi Burgiel

Posts: 44
Registered: 12/3/04
A single tile that generates an aperiodic tiling
Posted: Jan 24, 1995 8:06 AM
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I asked Professor Grunbaum about "Petra" and her tile, and he gave me
the following information:

"Petra" is Petra Gummelt, of Greifswald.

Her tile is based on the "Cartwheel decagon", which Professor Conway
proved cover every Penrose triangle tiling (Grunbaum & Shephard, p.
559). As I understand it, she colors the cartwheel in such a way that
when colored regions overlap exactly a Penrose tiling is generated.

So, the decagons don't really tile the plane. They overlap according
to some matching rules, and the resulting planar pattern is aperiodic.

It seems that the work was motivated by questions about the atomic
structure of "quasicrystals" of aluminum alloys.

I hope she will join the list and comment on this in person.

Heidi B.

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