Figure 3
From: Detection of oriented fractal scaling components in anisotropic two-dimensional trajectories
Orientation decomposition of the mixed fGn model (Eq. (6)) with \(H_1=0.8\), \(\theta _1=\pi /6=30^{\circ }\), \(H_2=0.6\), and \(\theta _2=4\pi /9=80^{\circ }\). (a) Sample path of \((x_{1}, x_{2})\). (b) Angle dependence of \(\log _{10} F^{(\theta )} (\tilde{s})\) vs. \(\log _{10} \tilde{s}\), where \(\tilde{s}=s/1.93\) in the second-order DDMA. (c) Angle dependence of the local slopes of \(\log _{10} F^{(\theta )} (\tilde{s})\) vs. \(\log _{10} \tilde{s}\). (d) Angle dependence of the slope in the range of \(1< \log _{10} \tilde{s} < 3\). (e) Reconstructed components \((\hat{\epsilon }_{1}, \hat{\epsilon }_{2})\). (f) Fluctuation functions of the reconstructed components of \(\hat{\epsilon }_{1}\) with \(\theta _{1} = 31^{\circ }\) and \(\hat{\epsilon }_{2}\) with \(\theta _{2} = 82^{\circ }\); the slopes in the range of \(1< \log _{10} \tilde{s} < 3\) were 0.8 and 0.6, respectively, in the second-order DDMA.
