The Fractality and Size Distributions of Astrophysical Self-Organized Criticality Systems

Abstract The statistics of nonlinear processes in avalanching systems, based on the self-organized criticality (SOC) concept Bak et al. (1988), predicts power-law-like size (or occurrence frequency) distribution functions. Following up previous work, we define a standard SOC model terms six assumptions: (i) area fractality, (ii) volume (iii) flux–volume proportionality, (iv) classical diffusion, (v) Euclidean maximum at event peak time, and (vi) spatiotemporal fluence or energy an avalanche event. We gather data fractal dimension power-law slopes from 162 publications assemble them 28 groups (for instance, solar flare energies, stellar energies), which find that 75% are consistent with model. Alternative models (Lévy flight, flat-world, nonfractal) slightly less correlated data. Outliers attributed to small number statistics, background definition problems, inadequate fitting ranges, deviations ideal power laws.