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Vincent A. Billock, Paul R. Havig, Brian H. Tsou; Dynamic fractal (1/f) noise as a driving force for hallucinatory pattern formation. Journal of Vision 2001;1(3):439. doi: 10.1167/1.3.439.
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© ARVO (1962-2015); The Authors (2016-present)
MacKay (Nature, 1957) describes three ways to visualize an odd opponency between certain spatial patterns. In the most studied of these MacKay effects, a transparency of a concentric circular or fan-shape pattern is superimposed on spatiotemporal white noise (e.g., TV ‘snow’). Viewed through a circular transparent pattern, the noise appears to stream radially; but through a fan-shape pattern the same noise streams in a circular fashion. We've shown that a similar opponency can be produced in flicker-induced hallucinations; by ‘seeding’ a flickering Ganzfeld with one form, the illusory opponent form is produced adjacently (apparently by a kind of simultaneous contrast; Billock et al., ARVO, 1999). We linked these hallucinations to a nonlinear dynamic phenomenon: self-organized pattern formation. Because of a connection between 1/f noise and nonlinear dynamic systems, we wondered what effect using filtered 1/f^a (pink) noise would have on the MacKay effect. We filtered spatiotemporal white noise to have fractal amplitude spectra A(fs,ft) = k/((fs^a)(ft^b)). Subjects viewed these fractals through concentric circular and fan-shape patterns. For white noise (a=b=0), all subjects replicated MacKay's results; orthogonal streaming was observed. This result persists for low values of the spatial exponent (a), but at high values of the spatial exponent, actual pattern formation occurs and subjects report hallucinatory fan-shapes and circles similar to those we reported previously for biased flicker-induced hallucinations. For hallucinatory fan-shapes driven by temporal spectra with low temporal exponents (b) subjects report streaming, but at higher values subjects report that the illusory arms appear to rotate. Because (due to the nonlinear retinocortical mapping function) concentric circular and fan-shape patterns map to cortex as simple, mutually orthogonal gratings, illusory pattern formation may be well suited for functional imaging studies.
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