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Ruben Verresen
Ruben Verresen
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Is this a quasi-crystal and/or a fractal?

I'm not too familiar with quasi-crystals, but I was recently playing around with a particular discrete function and I got the following neat pattern:

crystal

This is just a small segment, but as far as I could tell it does not become periodic. So I am wondering whether this is a quasi-crystal. More exactly:

  1. How would I go about figuring out whether or not this is a quasi-crystal?
  2. Does anyone recognize this pattern?

Knowing of the peculiar diffraction patterns of quasi-crystals, I took the Fourier transform of the above and obtained the following (again just showing a segment):

fourier transformation

(Details: this is in log-scale, with bright colors denoting high values, dark low values)

I find this quite beautiful and hence I'd love to have a better understanding of what's going on. In particular it seems to me that this might be a fractal. Again I am wondering how to formalize this and/or what the best way would be to advance if I want to 'understand' either of these patterns. Basically I'm not sure what to 'look for', which also makes it hard to make my question very concrete.

Is this a quasi-crystal and/or fractal?

I'm not too familiar with quasi-crystals, but I was recently playing around with a particular discrete function and I got the following neat pattern:

crystal

This is just a small segment, but as far as I could tell it does not become periodic. So I am wondering whether this is a quasi-crystal. More exactly:

  1. How would I go about figuring out whether or not this is a quasi-crystal?
  2. Does anyone recognize this pattern?

Knowing of the peculiar diffraction patterns of quasi-crystals, I took the Fourier transform of the above and obtained the following (again just showing a segment):

fourier transformation

I find this quite beautiful and hence I'd love to have a better understanding of what's going on. In particular it seems to me that this might be a fractal. Again I am wondering how to formalize this and/or what the best way would be to advance if I want to 'understand' either of these patterns. Basically I'm not sure what to 'look for', which also makes it hard to make my question very concrete.

Is this a quasi-crystal and/or a fractal?

I'm not too familiar with quasi-crystals, but I was recently playing around with a particular discrete function and I got the following neat pattern:

crystal

This is just a small segment, but as far as I could tell it does not become periodic. So I am wondering whether this is a quasi-crystal. More exactly:

  1. How would I go about figuring out whether or not this is a quasi-crystal?
  2. Does anyone recognize this pattern?

Knowing of the peculiar diffraction patterns of quasi-crystals, I took the Fourier transform of the above and obtained the following (again just showing a segment):

fourier transformation

(Details: this is in log-scale, with bright colors denoting high values, dark low values)

I find this quite beautiful and hence I'd love to have a better understanding of what's going on. In particular it seems to me that this might be a fractal. Again I am wondering how to formalize this and/or what the best way would be to advance if I want to 'understand' either of these patterns. Basically I'm not sure what to 'look for', which also makes it hard to make my question very concrete.

Source Link
Ruben Verresen
Ruben Verresen
  • 607
  • 5
  • 12

Is this a quasi-crystal and/or fractal?

I'm not too familiar with quasi-crystals, but I was recently playing around with a particular discrete function and I got the following neat pattern:

crystal

This is just a small segment, but as far as I could tell it does not become periodic. So I am wondering whether this is a quasi-crystal. More exactly:

  1. How would I go about figuring out whether or not this is a quasi-crystal?
  2. Does anyone recognize this pattern?

Knowing of the peculiar diffraction patterns of quasi-crystals, I took the Fourier transform of the above and obtained the following (again just showing a segment):

fourier transformation

I find this quite beautiful and hence I'd love to have a better understanding of what's going on. In particular it seems to me that this might be a fractal. Again I am wondering how to formalize this and/or what the best way would be to advance if I want to 'understand' either of these patterns. Basically I'm not sure what to 'look for', which also makes it hard to make my question very concrete.