Doesn't this follow from the fact that any Penrose tiling is an "expansion" of one with larger tiles, combined with the trivial fact that the theorem is trivially true for a single tile? I don't see how this gives you the strong form, though. Andy On Tue, May 20, 2014 at 8:18 AM, James Propp <jamespropp@gmail.com> wrote:
Can anyone provide a reference for Penrose's "local isomorphism theorem", asserting that every Penrose tiling looks like every other?
I seem to recall hearing a strong version of this stated once, to the effect that if you have a pattern of diameter n in one Penrose tiling, and you look for that pattern in a second Penrose tiling, you won't have to travel further than distance 2n.
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