Scaling collapse in the grid model.

<p>(Panel a) <i>p</i>(<i>t</i>|<i>l</i>) distribution for some values of path length <i>l</i>. Solid lines refers to the fitted log-normal distributions. (Panel b) Distribution of the scaled variable calculated at different values of <i>l</i>. The solid black line is the curve in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0143799#pone.0143799.e006" target="_blank">Eq (2)</a>. The Kolmogorov-Smirnov test rejects the hypothesis of the universal curve being a log-normal distribution. All the paths are sampled using intermediate steps on a 100 × 100 grid with <i>N</i>_shortcut = 100 and a fixed speed on each shortcut <i>v</i> = 3.0.