FIG. 3.

(Color online.) A) We define avalanches as excursions above a threshold S^*, with duration d the length of the excursion and size a the integral under the curve over the duration of the excursion. B) Distributions of avalanche size are power law for all α, P(a) ~ a^−3/2. The dashed line corresponds to sizes from a critical Galton-Watson branching process with S^* = 128. C) Durations are not power-law distributed but have the same distribution as durations from a critical Galton-Watson process. Durations do not show the familiar universal power-law exponent of −2 due to the conversion of ceaseless time series into avalanches (see text and [23]). Data shown: N = 10⁴ nodes over 3 × 10⁶ timesteps, 〈k〉 = 200.