Calculates the fractal dimension (D) of a trajectory using the
'dividers' method (Sugihara & May, 1990). By default, overestimation of
D is compensated for as recommended by Nams (2006), by walking the
dividers backwards and forwards, and by estimating the remaining path length
at the end of the last step.
TrajFractalDimension(trj, stepSizes, adjustD = TRUE, dMean = TRUE)The fractal dimension of the trajectory for the given step sizes.
Trajectory to calculate fractal dimension for.
Vector of step sizes (aka divider sizes) used to calculate path lengths.
If TRUE, path length is adjusted for truncation error
(Nams, 2006).
If TRUE, the fractal dimension is calculated starting
from the beginning of the trajectory, then re-calculated starting from the
end and moving backwards. The value returned is the mean of the two fractal
dimensions (Nams, 2006).
Fractal dimension may be meaningless for animal trajectories as they may not be true fractal curves - see Benhamou (2004) and Turchin (1996), although it may be useful for studies involving differences in behaviour at different spatial scales (Nams, 2006).
You can test whether a trajectory is a fractal curve for a range of step
sizes using the TrajFractalDimensionValues function. The
example code in its documentation demonstrates how to plot path length for a
range of step sizes. If the plotted points lie along straight line, then the
trajectory is a fractal curve for that range of step sizes. However, typical
trajectories result in a curve rather than a straight line.
If you decide to use fractal dimension despite the warnings of Benhamou (2004) and Turchin (1996), try to select a biologically meaningful range of step sizes (and be prepared to justify your choice). If comparing fractal dimensions across trajectories, be consistent in your choice of step sizes.
Benhamou, S. (2004). How to reliably estimate the tortuosity of an animal's path. Journal of Theoretical Biology, 229(2), 209-220. doi:10.1016/j.jtbi.2004.03.016
Nams, V. O. (2006). Improving Accuracy and Precision in Estimating Fractal Dimension of Animal movement paths. Acta Biotheoretica, 54(1), 1-11. doi:10.1007/s10441-006-5954-8
Sugihara, G., & M. May, R. (1990). Applications of fractals in ecology. Trends in Ecology & Evolution, 5(3), 79-86. doi:10.1016/0169-5347(90)90235-6
Turchin, P. (1996). Fractal Analyses of Animal Movement: A Critique. Ecology, 77(7), 2086-2090. doi:10.2307/2265702
TrajLogSequence to create a logarithmically spaced
sequence, TrajFractalDimensionValues for the function used
internally to calculate a range of path lengths for different step sizes,
TrajEmax and TrajSinuosity2 for some alternate
measures of trajectory tortuosity.