Fig. 2. Spatial and temporal self-similarity and correlation in switching activity.

(A) Percolating devices produce complex patterns of switching events that are self-similar in nature. The top panel contains 2400 s of data, with the bottom panels showing segments of the data with 10, 100, and 1000 times greater temporal magnification and with 3, 9, and 27 times greater magnification on the vertical scale (units of G₀ = 2e²/h, the quantum of conductance, are used for convenience). The activity patterns appear qualitatively similar on multiple different time scales. (B and E) The probability density function (PDF) for changes in total network conductance, P(ΔG), resulting from switching activity exhibits heavy-tailed probability distributions. (C and F) IEIs follow power law distributions, suggestive of correlations between events. (D and G) Further evidence of temporal correlation between events is given by the autocorrelation function (ACF) of the switching activity (red), which decays as a power law over several decades. When the IEI sequence is shuffled (gray), the correlations between events are destroyed, resulting in a significant increase in slope in the ACF. The data shown in (B) to (D) (sample I) were obtained with our standard (slow) sampling rate, and the data shown in (E) to (G) (sample II) were measured 1000 times faster (see Materials and Methods), providing further evidence for self-similarity.