With the Cosmic Web in Mind..

Some time ago I posted one of my Astronomy Look-alikes about the remarkable similarity between the structure of the human brain and that revealed by computer simulations of the large-scale structure of the Universe:

I wonder whether this means that the Cosmic Web is really just all in the mind?

Anyway I just came across an article by Franco Vazza and Alberto Fenetti that takes the comparison between brain cells (among other things) and the Cosmic Web a bit further, including a look at the corresponding power spectra:

The main point to take from this picture is that many naturally occurring patterns have approximately power-law power spectra, at least over a limited range of scales. However, as I have pointed out before on this blog, the power spectrum on its own does not really quantify pattern in any meaningful way. Here for example are two patterns with exactly the same power spectrum:

The point is that the power spectrum does not contain any information about the phase correlations of the Fourier modes, which are important in quantifying localised features. For further discussion of this issue, see here.

4 Responses to “With the Cosmic Web in Mind..”

  1. Although I agree entirely about the “devaluing” of phase spectra in pattern analysis, I’d quibble — well, more than quibble — with the idea that a power spectrum doesn’t quantify pattern in any meaningful way. Peaks in a power spectrum (or, equivalently, scattering/diffraction pattern) quantify a central aspect of any structure: its characteristic wavelength(s)/wavevector(s).

    Let’s not throw the baby out with the bathwater!

    “…many naturally occurring patterns have approximately power-law power spectra, at least over a limited range of scales.

    That proviso is too often omitted. There’s been a little too much over-exuberance about power law scaling over the years. This is a great post on that topic: So You Think You Have a Power Law? — Well, Isn’t That Special

  2. Wow ! neat stuff ! I do not understand your words, though.

  3. Can everyone see the first image?

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