<p>As indicated above each frame, the beating patterns that generated a true linear path were those where the right and left middle legs (<i>m<sub>r</sub></i>+<i>m<sub>l</sub></i>), hind legs (<i>h<sub>r</sub></i>+<i>h<sub>l</sub></i>), and hind followed by middle legs (<i>h<sub>r</sub></i>+<i>h<sub>l</sub></i>, <i>m<sub>r</sub></i>+<i>m<sub>l</sub></i>) beat simultaneously. In these three cases, the total distance traveled was equal to Δy. For the other three cases where the middle right and left legs (<i>m<sub>r</sub></i>, <i>m<sub>l</sub></i>) and the hind right and left legs (<i>h<sub>r</sub></i>, <i>h<sub>l</sub></i>) beat alternately, and the simultaneous beating of the hind legs followed by the beating of a middle leg (<i>h<sub>r</sub></i>+<i>h<sub>l</sub></i>, <i>m<sub>r</sub></i>, <i>h<sub>r</sub></i>+<i>h<sub>l</sub></i>, <i>m<sub>l</sub></i>) the net forward distance traveled was calculated from a line between the start and end point. Numerical analysis of these trajectories is shown in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002792#pcbi-1002792-t004" target="_blank"><b>Table 4</b></a>.</p