قارن الطرق

	تحليل الكسور (Fractal Analysis)	إنتروبيا العينة
المجال	الأنظمة المعقدة	الأنظمة المعقدة
العائلة	Machine learning	Machine learning
سنة النشأة	1983	2000
صاحب الطريقة	Benoit Mandelbrot	Richman & Moorman
النوع	Geometric complexity quantification	Nonlinear entropy measure
المصدر التأسيسي	Mandelbrot, B. B. (1983). The Fractal Geometry of Nature. W. H. Freeman. ISBN: 978-0-7167-1186-5	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.
الأسماء البديلة	Box-Counting Analysis, Fractal Dimension Estimation, Multifractal Analysis, Fraktal Analiz	SampEn, Sample Entropy (SampEn), Örneklem Entropisi, Nonlinear Complexity Measure
ذات صلة	2	2
الملخص	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.	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.