Matlab, R and free software for trajectory analyses in ichnology

The original free software has some output issues, and is fixed in: https://zenodo.org/records/19481550 These are the MATLAB and R codes, and a free software for trajectory analysis of a fossil trail. Trajectory.m and Trajectory.R analyze trajectory-related metrics, including turning-angle series, frequency spectra (single-sided representation), autocorrelation functions, the minimal normalized radius of curvature, the smoothness index, and the Shannon index, etc., based on a series of (x, y) coordinates (such as the two series of values x, y in the attached "Coordinates.txt"). Fractal_index.m and Fractal_index.R compute the fractal index from an image in which the trajectory is shown in black against a white background (such as the attached "Forage.tiff"). It should be noted that, for smoothness analyses, the minimal value of F is 2 by definition (of smoothness index), which is also the standard choice. Although F can be set slightly higher, the manuscript “Reproducing and understanding a fossil trail in digitized worlds: a protocol to quantitative analyses of movement trajectories” (doi: 10.1080/10420940.2026.2642060) shows that excessively large F values introduce substantial noise. Fractal analysis has not been integrated into the free software Trajectory Analysis_Version3. And to ensure best accuracy, the length of the turning angle series (N-2) is two steps shorter than the length of the points series (number of extracted points, N) in the codes and the free software. The input data for the free software should only contain two columns of values. For example, for "Coordinates.txt", one should remove the heads "Generated by GetData ......Line #1".