Shiner–Davison–Landsberg complexity revisited

Shiner, Davison and Landsberg have recently proposed a measure of complexity that has become the subject of an intense debate. We show that using the framework of the thermodynamic formalism, the properties and shortcomings of this measure—over-universality and a trivial implementation of the temperature dependence—can be interpreted and elucidated in a coherent way. Moreover, we show how the SDL approach can be refined to nullify these critiques. Results of the logistic parabola family demonstrate the improved behaviour of the modified SDL measure of complexity. For the tent map family, an interesting linear dependence of the modified measure as a function of the asymmetry is observed.