手法を比較

	フラクタル解析	再帰定量化解析 (RQA)
分野	複雑系	複雑系
系統	Machine learning	Machine learning
提唱年	1983	2007
提唱者	Benoit Mandelbrot	Marwan, Romano, Thiel & Kurths
種類	Geometric complexity quantification	Nonlinear time-series characterization
原典	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.
別名	Box-Counting Analysis, Fractal Dimension Estimation, Multifractal Analysis, Fraktal Analiz	RQA, Recurrence Plot Analysis, Nonlinear Recurrence Analysis, Tekrarlama Kantifikasyon Analizi
関連	2	2
概要	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.