Wikipedia:Reference desk/Archives/Mathematics/2006 October 13

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Penrose tiling, and its Fourier transform

What does the 2D fourier transform of a penrose tiling look like? --HappyCamper 12:27, 13 October 2006 (UTC)[reply]

I'd expect that instead of nice spikes at the relevant frequency vectors, there would be wild oscillation. Surely there would be something. Melchoir 19:02, 13 October 2006 (UTC)[reply]

Probably, you need to be more specific about what you actually mean with a Penrose tiling, that is, how you intend to draw it on the plane. The article itself shows several different ways to do so. I think that if you draw them with infinitely thin lines, they would not have any impact at all in the Fourier transform, which would be just zero. And how about different colours? —Bromskloss 22:21, 13 October 2006 (UTC)[reply]

This is an excellent question that deserves more than cop-outs. Here's an image (which, unfortunately, you might not be able to see without a subscription), and these articles also have some nice diagrams. —Keenan Pepper 06:37, 14 October 2006 (UTC)[reply]

I'm sure it's a good question, I just don't know how the image is defined! —Bromskloss 20:16, 15 October 2006 (UTC)[reply]