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Vincent A Billock, Brian H Tsou; A special case of the MacKay effect generates geometric hallucinations: Stochastic resonance in pattern formation driven by fractal (1/f) noise. Journal of Vision 2003;3(9):350. doi: https://doi.org/10.1167/3.9.350.
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© ARVO (1962-2015); The Authors (2016-present)
PURPOSE: We've been studying spatial opponency in flicker-induced geometric hallucinations (fan shaped “seeds” in a flickering field induce illusory concentric circles and vice versa). A version of the MacKay effect (Nature, 1957) shows a similar opponency — if white noise (e.g., TV static) is viewed through a geometric transparency (e.g., a set of concentric circles) the motion of the white noise appears to be orthogonal to the orientation of the transparency. However, we (VSS, 2001) found that illusory spatial patterns (e.g., rotating fans or pulsing circles) form in the noise viewed through the transparency, if the noise is not “white”. To study this effect we used dynamic fractal noise. METHODS: Three observers viewed noise that is 1/f^a in space and 1/f^b in time through a geometric mask that is either a set of concentric circles or a pattern of pie-like wedges. Subjects used the method of adjustment to find the lowest RMS contrast at which illusory geometric patterns appear in the noise. RESULTS: All subjects had much lower thresholds for filtered noise than for white noise; for most conditions pattern formation occurs most easily for spatial exponents of about 1.0–1.3 and temporal exponents around 1.0. DISCUSSION: There is a phenomenon known as stochastic resonance, in which noise has an effect on a nonlinear system or signal. In physics there are three kinds of stochastic resonance: noise amplification of a signal, noise induction of multistability, and noise induction of pattern formation. This last case has never been documented outside of mathematical systems; the effect we describe may be the first known physical manifestation of pattern formation by stochastic resonance. In all types of stochastic resonance, some nonlinear systems prefer 1/f noise and there is a strong link between 1/f spectra and pattern formation in many physical systems.
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