Dependence of the complexity-entropy causality plane on Hurst exponent <i>h</i>.

<p>We have employed fractal surfaces of size (). In (a) we plot and versus for the embedding dimensions and (circles) and also for and (squares). We note the invariance of the index against the rotation and . In (b) we plot the diagram for . We observe changes in the scale of and caused by the increasing number of states. In both cases, as increases the complexity also increases while the permutation entropy decreases. This behavior reflects the differences in the roughness shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0040689#pone-0040689-g002" target="_blank">Fig. 2</a>. For values of the surface is anti-persistent which generates a flatter distribution for the values of leading to values of and closer to the aleatory limit ( and ). For values of there is a persistent behavior in the surfaces heights which generates a more intricate distribution of and, consequently, values of and that are closer to the middle of the causality plane (region of higher complexity).