Figure 12.

Breakpoints and crossover scales of superposition-type bimodality cannot possibly be identical. (A) Component scaling functions (fractal and noise) applied in Figures 3, 4 were used (solid black) to demonstrate the discrepancy in the underlying fractal components estimated by qSRA-FMF (light gray) and SFD-FMF (gray) methods. (B) The vicinity around the true crossover is shown enlarged. Note the difference between the true crossover scale and its estimate by SFD-FMF and the breakpoint estimated by qSRA-FMF. The former is due to the limited precision of the estimation by SFD-FMF, which both in principle and practice can be decreased. The latter cannot be minimized by improving the precision of qSRA-FMF owing to conceptual limitations preventing minimization of the difference between the true crossover scale and its estimation by a breakpoint. (C) Composite scaling functions were obtained by superpositioning the component time series (black line) or by applying the best fitted scheme of SFD-FMF and qSRA-FMF methods, respectively.