(a, top) Tangent angle, is the angle between and the average direction of motion of the animal, . (bottom) Example space-time plot of , corresponding to the bottom trial in c. The diagonal bands indicate a head-to-tail traveling wave propagated at constant speed. (b) The two dominant PCs representing . The solid lines are the experimental results, the dashed lines are sine fits to . Coefficients with 95% confidence bounds were , , , , , . Both vectors were divided by the same maximum value such that the maximum amplitude was one. These two PCs account for 91% of the variance. (c) The amplitudes and associated with the PCs in e. Color indicates the frame number for all trials (N = 9, n = 30) combined. The trajectories move counterclockwise around the circular structure, indicating a traveling wave. The radius of this circle is the amplitude of the wave of . See Stephens et al., 2008.