Fig. 4. Demonstration of criticality.

Estimates of three independent measures of 1/σνz are obtained from the crackling relationship (green), plots of mean avalanche size given duration (blue), and avalanche shape collapse (cyan). The blue, cyan, and green symbols agree within the measurement uncertainty in almost every case. Each panel also shows the power law exponents of avalanche size (τ; red) and avalanche duration (α; amber). (A) Critical exponents for sample I over a range of low voltages and for a combined dataset (low sampling rate; see Materials and Methods), showing that the critical exponents are substantially independent of voltage. (B) Comparison of critical exponents measured for sample II for repeated, independent 6 V DC measurements (fast sampling rate; see Materials and Methods). (C) Critical exponents for sample III as a function of voltage (slow sampling rate). (D) Data from a second sequence of measurements on sample III identical to that in (C), showing that while the exponents α and τ vary because of internal reconfigurations of the percolating device, the three estimates of 1/σνz remain in good agreement at every voltage. (E and F) Voltage-dependent data from sample IV (E and F, fast and slow sampling rates, respectively), showing that criticality and self-similarity are observed on vastly different time scales. The mean values of 1/σνz were found to be 1.46 ± 0.05, 1.40 ± 0.03, and 1.40 ± 0.04 from the crackling relationship, 〈S〉(T) and shape collapse, respectively (uncertainties are 1 SD), indicating that there is no significant difference between the estimates from the three independent methods. This is confirmed by a single-factor analysis of variance (ANOVA) test (P = 0.47). The (τ, α) data are replotted in fig. S6 to allow a different comparison with the three calculations of 1/σνz (27).