Fig 1.
Exponents q for which multifractal analysis met the r < .995 benchmark for Eqs 3 and 4.
Plot of individual series’ multifractal analysis indicating, on the y-axis, how many values of q served to produce stable power-law relationships in Eqs 3 and 4 and, on the x-axis, the resulting width of the multifractal spectrum. Because q is effectively a distortion serving to reveal differences in the temporal structure, less multifractal series should withstand a wider range of q and generate more similar and all equally stable scaling relationships in Eqs 3 and 4. However, more multifractal series will have more heterogeneous structure that will be more likely to generate deviations in and eventually weaknesses in power-law relationships with smaller changes in q.
Fig 2.
Scaling relationships for Eq 3 for the Wind condition.
Plot of the negative Shannon entropy on y-axis against logarithmic time scale for an example postural-displacement series in the Wind condition for each of 7 values of q.
Fig 3.
Scaling relationships for Eq 3 for the No-Wind condition.
Plot of the negative Shannon entropy on y-axis against logarithmic time scale for an example postural-displacement series in the No-Wind condition for each of 9 values of q.
Fig 4.
Plot of model predicted WBLOCK over four 20-s (1000-frame) blocks for phasmids with high WALL (solid lines) and with low WALL (dashed lines) under the conditions of wind stimulation (black lines) or no-wind stimulation (grey lines). In all cases, “high” and “low” were defined as the third and first quartiles in corresponding conditions. WBLOCK was initially much greater at the onset of wind stimulation, but it decreased smoothly across blocks, showing a quicker decrease for phasmids who had lower multifractal spectrum width across their whole series. Phasmids in the no-wind condition showed initially much lower WBLOCK and only very shallow increase of WBLOCK with progressive blocks.
Table 1.
Regression model predicting the changes in WBLOCK, multifractal spectrum width for consecutive 1000-frame portions of the postural displacements.
Fig 5.
Plot of model predicted tBLOCK over four 20-s (1000-frame blocks for phasmids with positive tALL (solid lines) and with negative tALL (dashed lines) under the conditions of wind stimulation (black lines) or no-wind stimulation (grey lines). In all cases, “positive” and “negative” settings of tALL for these plots were defined as the third and first quartiles of tALL in corresponding conditions. tBLOCK was effectively flat across all blocks of wind stimulation, with the exception of a significant decrease (e.g., to -2.10 for the third quartile tALL in wind stimulation). Phasmids in the no-wind condition showed tBLOCK comparable to their tALL in the first block. Subsequent blocks without wind stimulation showed negative tBLOCK for all cases on Blocks 2 and 3, increasing on Block 4.
Table 2.
Regression model predicting the changes in tBLOCK, multifractal spectrum width due to nonlinearity for consecutive 1000-frame portions of the postural displacements.