مقایسهٔ روش‌ها

	خودسازمان‌دهی بحرانی	تحلیل فرکتالی	تحلیل کمی بازگشت (RQA)
حوزه	سیستم‌های پیچیده	سیستم‌های پیچیده	سیستم‌های پیچیده
خانواده	Regression model	Machine learning	Machine learning
سال پیدایش	1987	1983	2007
پدیدآور	Per Bak, Chao Tang & Kurt Wiesenfeld	Benoit Mandelbrot	Marwan, Romano, Thiel & Kurths
نوع	Dynamical systems model	Geometric complexity quantification	Nonlinear time-series characterization
منبع بنیادین	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	Marwan, N., Romano, M. C., Thiel, M., & Kurths, J. (2007). Recurrence plots for the analysis of complex systems. Physics Reports, 438(5–6), 237–329.
نام‌های دیگر	SOC, Sandpile Model, Critical Self-Organization, Kendiliğinden Örgütlenen Kritiklik	Box-Counting Analysis, Fractal Dimension Estimation, Multifractal Analysis, Fraktal Analiz	RQA, Recurrence Plot Analysis, Nonlinear Recurrence Analysis, Tekrarlama Kantifikasyon Analizi
مرتبط	3	2	2
خلاصه	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.	Recurrence Quantification Analysis (RQA) is a nonlinear method for characterizing the dynamics of a time series by quantifying the small-scale structure of its recurrence plot. Introduced in its modern, comprehensive form by Marwan, Romano, Thiel, and Kurths in 2007, RQA extracts scalar measures — such as recurrence rate, determinism, laminarity, and Shannon entropy — that capture periodicity, chaos, stationarity, and transitions in complex dynamical systems.