Matlab, R and free software for trajectory analyses in trace fossils

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, minimal normalized body length estimation, etc., based on a series of (x, y) coordinates (such as the two series of values x, y in the attached "Coordinates1.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. You will need to wait for a few seconds before the software opens. AN UPDATED SOFTWARE INTEGRATED WITH MORE FUNCTIONS IS AVAILABLE AT: https://zenodo.org/records/20134095 which is supplemented to Wang & Shi, PNAS, 2026 (doi: 10.1080/10420940.2026.2642060).