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The Badlands Guardian is a geomorphological feature; see this website. According to Wikipedia, this figure has been created by natural processes. However, my intuition says that the chance that this happens is small.

Could one make a model of the geological processes in this area, and also make an estimate when an image looks 'good enough' like a human? Then it might be possible to calculate the chance that such a coincidence occurs.

EDIT: the idea of this question is similar to the approach to debunk Ley Lines by considering alignments of random points.

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    $\begingroup$ Humans are very good at recognizing human faces -- even when there are no humans around. We see faces in clouds, faces in rock formations, and even faces on Mars. $\endgroup$ Mar 10 at 14:21
  • $\begingroup$ Yeah, I saw the face on Mars. When you view it from the side, it doesn't look like a face at all $\endgroup$
    – Riemann
    Mar 10 at 14:25
  • $\begingroup$ However, the Badlands Guardian seems pretty correct $\endgroup$
    – Riemann
    Mar 10 at 14:26
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    $\begingroup$ Try rotating the image in Google maps - the face disappears! It's just a good example of a Mimetolith, a subset of Pareidolia, and no different to seeing an animal in clouds or the man in the moon. $\endgroup$
    – Andy M
    Mar 10 at 16:50
  • $\begingroup$ This sounds very similar to von Storch and Zwiers' "Mexican hat fallacy", just a different rock formation. You've already implicitly used the rareness (uniqueness?) of the feature to form the hypothesis, testing it statistically just tells you what you already know, it's rare! $\endgroup$
    – Deditos
    Mar 10 at 16:59

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The chance that this occurs in this particular spot is indeed small. The chance that a natural face-like feature occurs somewhere on the earth's hundreds of millions of square miles of land area is virtually guaranteed. Even if the chance of natural face formation in an area this size is one in a billion, it's utterly unsurprising to find a few faces scattered around the globe.

I don't think you'll be able to model the geological and pattern recognition processes to generate a probabilistic estimate that's more precise than one part in a billion. There isn't any evidence to suggest that this formation is anything but natural, and unless your geological model can accurately state that the likelihood of such a face in such an area is less than 0.0000001%, we should not be surprised to find a formation that looks like a face when looking at hundreds of millions of square miles of land area. At that level of precision, variability due to your choice of assumptions for the modeling are likely to dwarf any meaningful output of the model.

Pareidolia is the phenomenon of perceiving meaningful patterns where there are none. It's extremely common to see meaningful shapes in natural formations like clouds and rocks, even though the formations are natural and random. With nothing to suggest any kind of active sculpting of this formation (nothing to suggest by whom, or how, or when, or for what purpose it was sculpted), the most likely explanation is natural formation and pareidolia.

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  • $\begingroup$ If you take the extremely simple model where the picture consists of 100 times 100 pixels and each pixel is randomly assigned 1 out of 100 colors, then 1 million samples will already give a very detailed picture of a human somewhere $\endgroup$
    – Riemann
    Mar 10 at 17:17
  • $\begingroup$ I think you could word your first sentence better; some might interpret it as supporting OP's implied hypothesis. $\endgroup$
    – Spencer
    Mar 13 at 14:37

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