Fractal correlation in heterogeneous systems

摘要: Abstract Noisy or irregular signals are usually thought of as being composed driven by random processes. However, some which appear noisy (such fractal signals) correlated, and the dimensions, D, provides a measure degree correlation between elements (densities, intensities property, voltages, etc.) over space time. To arrive at this correlation, methods analysis using dispersion signal, such relative Hurst rescaled range analysis, give measures dimension D two-point adjacent segments signal. We have derived expressions for an extended observations non-adjacent neighbors. The result allows estimation from autocorrelation function directly. use test self-similarity to determine whether not fall-off is same different sized groupings data. This means that estimate requires one unit size range-extended behavior, with verification other size. coefficient nth neighbor units rn=0.5[|n + 1|2H−2|n|2H |n−1|2H], where H = 2 − one-dimensional signals. Asymptotically, ratio successive values rnisrn/rn−1 [n/(n− 1)]2H−2. technique therefore both efficient relatively robust.