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Stare at the centre of the figure for a while. Some ‘scintillating’ activity will build up in the violet and blue annuli. Some observers also report a circular rotation within these regions; things will begin to "run around in circles”.
This image "The Enigma” is by Isia Leviant (1981).
Mechanism currently unknown (as far as I know, but see Zanker 2004), an ‘enigma’. Activity in MT (Zeki) is an interesting finding, but does not ‘explain’ the effect IMHO.
Zeki S, Watson JD, Frackowiak RS (1993) Going beyond the information given: the relation of illusory visual motion to brain activity. Proc R Soc Lond B Biol Sci 252:215–22
These pages demonstrate visual phenomena, and »optical« or »visual illusions«. The latter is more appropriate, because most effects have their basis in the visual pathway, not in the optics of the eye. When I find the time I will expand the explanations, to the degree that these phenomena are really understood; any nice and thoughtful comment welcome. You may be glad to know: There are no tasteless surprises here; you know, these infantile pranks where you scrutinize a picture and suddenly an ugly face (or the opposite end) screams at you… Don’t distress yourself if you don’t see the effect described, even if trying carefully. For many illusions, there is a small percentage of people with perfectly normal vision who just don’t see it, for reasons currently unknown.