قارن الطرق

	النشوء الذاتي للحرجية	تحليل الكسور (Fractal Analysis)
المجال	الأنظمة المعقدة	الأنظمة المعقدة
العائلة	Regression model	Machine learning
سنة النشأة	1987	1983
صاحب الطريقة	Per Bak, Chao Tang & Kurt Wiesenfeld	Benoit Mandelbrot
النوع	Dynamical systems model	Geometric complexity quantification
المصدر التأسيسي	Bak, P., Tang, C., & Wiesenfeld, K. (1987). Self-organized criticality: An explanation of 1/f noise. Physical Review Letters, 59(4), 381–384.	Mandelbrot, B. B. (1983). The Fractal Geometry of Nature. W. H. Freeman. ISBN: 978-0-7167-1186-5
الأسماء البديلة	SOC, Sandpile Model, Critical Self-Organization, Kendiliğinden Örgütlenen Kritiklik	Box-Counting Analysis, Fractal Dimension Estimation, Multifractal Analysis, Fraktal Analiz
ذات صلة	3	2
الملخص	Self-Organized Criticality (SOC) is a dynamical systems framework introduced by Per Bak, Chao Tang, and Kurt Wiesenfeld in 1987 to explain how large, dissipative systems spontaneously evolve toward a critical state without external fine-tuning. At the critical state, the system produces scale-invariant fluctuations — avalanches whose size and duration follow power-law distributions — and generates 1/f (pink) noise in its power spectrum.	Fractal Analysis quantifies the self-similar, scale-invariant complexity of geometric objects and time series through the fractal dimension D and the Hurst exponent H. Introduced systematically by Benoit Mandelbrot in his 1983 landmark work, the framework extends classical Euclidean geometry to irregular shapes found in nature, finance, physiology, and materials science. It provides a single dimensionless index that captures how completely a pattern fills space across multiple scales.