Abstract
The paper proposes two (2) measures for correlating fractal random variables. The correlation measures depict the extent to which roughness in one variable induces roughness to the other. The first measure, fractal correlation, directly uses the usual moment-based product moment correlation of the fractal measures λx and λy at each point (xi,yi). Each of the fractal measures are marginally exponentially distributed and so their second moments exist. The second measure, fractal geometric correlation, takes advantage of the fact that fractal curves may have infinite perimeters but they enclose finite areas A. The fractal geometric correlation is given by the reciprocal of (A+1)λ-1. Simulation results are given and applications in landscape ecology are provided.
Recommended Citation
Padua, Roberto N.; Mirasol, Joy M.; Palompon, Daisy R.; and Ontoy, Dexter S.
(2015)
"Correlating Two Fractal Random Variables: Application
To Animal Food Search Behavior,"
CNU Journal of Higher Education: Vol. 9:
Iss.
1, Article 5.
DOI: https://doi.org/10.70997/2546-1796.1115
Available at:
https://jhe.researchcommons.org/journal/vol9/iss1/5