Correlating Two Fractal Random Variables: Application to Animal Food Search Behavior

The paper proposed two (2) measures for correlating fractal random variables. The correlation measures depicted the extent to which roughness in one variable induces roughness in the other. The first measure, fractal correlation, directly used the usual moment-based product moment correlation of the fractal measures λx and λy at each point (xi ,yi). Each of the fractal measures was marginally exponentially distributed and so their second moments exist. The second measure, fractal geometric correlation, took advantage of the fact that fractal curves may have infinite perimeters but they enclosed finite areas A. The fractal geometric correlation was given by the reciprocal of (A+1)λ-1. Simulation results were given and applications in landscape ecology were provided.