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)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, the re-calculated starting from the
end and moving backwards. The value returned is the mean of the two fractal
dimensions (Nams, 2006).
The fractal dimension of the trajectory for the given step sizes.
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).
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.