To me, it's basically p-hacking. Because the it starts with human artifacts the similarity is more on the level of finding that two English language texts have similar letter frequencies and presenting it as an episode of Ancient Aliens.

http://freakonometrics.hypotheses.org/19817

Eh, I disagree. Power spectra are a pretty standard thing to use to compare e.g. different structure formation models in Cosmology and I still stand by the idea that the two are strikingly similar (and how interesting that is).