TrajFractalDimension: Fractal dimension of a trajectory

In JimMcL/trajr: Animal Trajectory Analysis

Fractal dimension of a trajectory

Description

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.

Usage

TrajFractalDimension(trj, stepSizes, adjustD = TRUE, dMean = TRUE)

Arguments

trj	Trajectory to calculate fractal dimension for.
stepSizes	Vector of step sizes (aka divider sizes) used to calculate path lengths.
adjustD	If TRUE, path length is adjusted for truncation error (Nams, 2006).
dMean	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).

Details

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.

Value

The fractal dimension of the trajectory for the given step sizes.

References

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

See Also

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.

JimMcL/trajr documentation built on July 23, 2024, 2:06 a.m.