Common examples are perceived images of animals, faces, or objects in cloud formations, the "man in the moon", the "moon rabbit", and hidden messages within recorded music played in reverse or at higher- or lower-than-normal speeds.
Pareidolia is the visual or auditory form of apophenia, which is the perception of patterns within random data. Combined with apophenia and hierophany (manifestation of the sacred), pareidolia may have helped ancient societies organize chaos and make the world intelligible.
The word is derived from the Greek words para (παρά, "beside, alongside, instead [of]", in this context meaning something faulty or wrong) and the noun eidōlon (εἴδωλον "image, form, shape", the diminutive of eidos).
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And see Alien UFO hunters spot a mouse on Mars, from Huffington Post, for another example