مقایسهٔ روش‌ها

	تحلیل فرکتالی	تحلیل کمی بازگشت (RQA)	آنتروپی نمونه (Sample Entropy)
حوزه	سیستم‌های پیچیده	سیستم‌های پیچیده	سیستم‌های پیچیده
خانواده	Machine learning	Machine learning	Machine learning
سال پیدایش	1983	2007	2000
پدیدآور	Benoit Mandelbrot	Marwan, Romano, Thiel & Kurths	Richman & Moorman
نوع	Geometric complexity quantification	Nonlinear time-series characterization	Nonlinear entropy measure
منبع بنیادین	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.	Richman, J. S., & Moorman, J. R. (2000). Physiological time-series analysis using approximate entropy and sample entropy. American Journal of Physiology, 278(6), H2039–H2049.
نام‌های دیگر	Box-Counting Analysis, Fractal Dimension Estimation, Multifractal Analysis, Fraktal Analiz	RQA, Recurrence Plot Analysis, Nonlinear Recurrence Analysis, Tekrarlama Kantifikasyon Analizi	SampEn, Sample Entropy (SampEn), Örneklem Entropisi, Nonlinear Complexity Measure
مرتبط	2	2	2
خلاصه	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.	Sample Entropy (SampEn) is a nonlinear measure of the complexity and regularity of a time series. Introduced by Richman and Moorman in 2000 as an improvement over Approximate Entropy (ApEn), it quantifies the likelihood that similar patterns of a given length in the series remain similar when extended by one additional data point. A higher SampEn value indicates greater irregularity and complexity, while a lower value indicates more regularity or self-similarity.