The statistical properties of the spontaneous background electrocorticogram (ECoG) were modeled, starting with random numbers, constraining the distributions, and identifying characteristic deviations from randomness in ECoG from subjects at rest and during intentional behaviors. The ECoG had been recorded through 8 x 8 arrays of 64 electrodes, from the surfaces of auditory, visual, or somatic cortices of 9 rabbits, and from the inferotemporal cortex of a human subject. Power spectral densities (PSD) in coordinates of log(10) power versus log(10) frequency of ECoG from subjects at rest usually conformed to noise in power-law distributions in a continuum. PSD of ECoG from active subjects usually deviated from noise in having peaks in log(10) power above the power-law line in various frequency bands. The analytic signals from the Hilbert transform after band pass filtering in the beta and gamma ranges revealed beats from interference among distributed frequencies in band pass filtered noise called Rayleigh noise. The beats were displayed as repetitive down spikes in log(10) analytic power. Repetition rates were proportional to filter bandwidths for all center frequencies. Resting ECoG often gave histograms of the magnitudes and intervals of down spikes that conformed to noise. Histograms from active ECoG often deviated from noise in Rayleigh distributions of down spike intervals by giving what are called Rice (Mathematical analysis of random noise-and appendixes-technical publications monograph B-1589. Bell Telephone Labs Inc., New York, 1950) distributions. Adding power to noise as signals at single frequencies simulated those deviations. The beats in dynamic theory are deemed essential for perception, by gating beta and gamma bursts at theta rates through enhancement of the cortical signal-to-noise ratio in exceptionally deep down spikes called null spikes.