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During a break n a seminar today, I noticed that the chairs in front of me all had slightly transparent black mesh fabric. The backs of the chairs were in the shape of a hyperbolic paraboloid. The fabric covering it had two layers a couple of centimeters apart (it was just a fabric sheath over a frame), and the mesh was a hexagonal tiling with hole size approximately equal to thread size, both small.

I noticed that the interference between the two meshes made a bullseye pattern. The circles in the bullseye moved inwards or outwards as I moved my head, but the center of the bullseye seemed to be constantly at the critical point of the hyperbolic paraboloid (although I couldn't move my head much from side to side).

Why did this shape appear?

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You may be referring to a Moire pattern – Jeremy Apr 5 '13 at 0:55
Yes, that's exactly what I'm referring to. I know that interference patterns occur(although the article really helped me understand it better), but my question is, why did it have that particular shape? – Brian Rushton Apr 5 '13 at 0:59
@Jeremy, it is amazing that you got it from just the description. – Lord Soth Apr 5 '13 at 1:33
I honestly couldn't quite figure out what picture you have in mind. I guess it is a bit late to ask whether you happened to take a photo of the pattern? – Willie Wong Apr 5 '13 at 15:48
@WillieWong: I didn't, but they are in the math seminar room at UPenn in the DRL (I think 4C8 or 4C28), in case anyone one here has time, lol. – Brian Rushton Apr 5 '13 at 15:57
up vote 1 down vote accepted

I have not seen the chairs in question, so below is just pure speculation. I suspect, but am not sure, that what you saw was a combination of two effects caused by the chair frame.

  1. Because the chair frame is a hyperbolic paraboloid, from where you sit the pattern of "holes" in the fabric appears effectively aperiodic while roughly uniformly distributed.
  2. Because the chair frame has a physical dimension, one layer of the chair fabric is further away from you then the other. From where you sit the layer that is further away from you appears to be "smaller".

Apparently if you start with an aperiodic screen pattern $A$ and produce a Moiré pattern based on $A$ and a rotation and/or rescaling $A'$, you tend to observe circular patterns. See figures 2.1c and 2.1e here. In general, I think you may be able to find an answer to your question in this book.

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Thanks! Looking back, it probably just looked like it was centered at the critical point since I was directly behind it. I've googled "black mesh office chair" and saw a lot of moire patterns, by the way. – Brian Rushton Apr 8 '13 at 14:36

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