We quantified the character and underlying nature of spectral changes in human brain electric potentials, while working with implanted cortical surface arrays in epileptic patients. In our initial motor movement study, we identified a broadband in the power spectrum at 76-100 Hz, which increased in power in a focal brain region during activity, in stark contrast to well known non-focal power decreases in the α/β rhythms at low frequencies 8-32 Hz. We observed that these changes also happened, albeit not as strongly, during movement imagery, but could be dramatically enhanced when we coupled imagery associated spectral changes to cursor-based feedback (a brain computer interface). We hypothesized that this broad band and the α/β rhythms represent different processes: the peaks originate from synchronous processes over large areas of the brain, while the broadband reveals temporally scale-free (asynchronous) changes associated with local neural computation. We were able to map local function in the brain, in real-time, by capturing broadband power changes in the 76-200 Hz "χ-band". After careful hardware characterization, we discovered that the cortical spectrum follows a power law of the form P ∼ f^-χ, where χ = 4.0 ± 0.1 between 80-500 Hz. The exponent shifts to χ _L = 2.0 ± 0.4 over all 10 ≤ f ≤ 500 Hz, after dividing out a Lorentzian crossover function (f ₀ = 70 Hz). In cortical areas associated with motor movement, a principal component-type decomposition removed the α/β rhythms, and find that only the amplitude of the power law, not the value of χ _L, changes with activity.