1/f Noise Characterized and Long-term Fractal Layers Described, in Anderson & Mandell, in Fractals of Brain, Fractals of Mind

by Corry Shores
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1/f Noise Characterized and Long-term Fractal Layers Described

Anderson & Mandell

Fractal Time and the Foundations of Consciousness

in

Fractals of Brain, Fractals of Mind

In 1/f noise,

Big events are less frequent than little events. "Twice as big occurs half as often." In general, 1/f noise is fractal with respect to time, because the same process "[...] pshsh, ktshs, pdk, kshsh [...]" occurring on one timescale, say microseconds, is identical to a "[...] pshsh, ktshs, pdk, kshsh [...]" occurring on another timescale of say minutes. Press (1978) describes these bunched clustering, correlated patterns as manifesting a primitive form of memory:

[there is] indirect evidence that the flicker noise in a carbon resistor, say, gives rise to fluctuations [in atomic clocks] coherent over times as long as 10^6 seconds. This is quite fantastic! How does the resistor remember over a period of weeks or months that it is in an 'up' fluctuation? (Press 1978:109)

(Anderson & Mandell 78-79)

Anderson, Carl M. & Arnold J. Mandell. Fractal Time and the Foundations of Consciousness: Vertical Convergence of 1/f Phenomena from Ion Channels to Behavior States. in Fractals of Brain, Fractals of Mind. Ed. Earl Mac Cormac & Maxim I. Stamenov. Amsterdam: John Benjamins Publishing Company, 1996.