Fractal Dimension, Walk Dimension and Conductivity Exponent of Karst Networks around Tulum

Understanding the complex structure of karst networks is a challenge. In this work, we characterize the fractal properties of some of the largest coastal karst network systems in the world. They are located near the town of Tulum (Quintana Roo, Mexico). Their fractal dimension d_f, conductivity exponent μ^∼ and walk dimension d_w are estimated using real space renormalization and numerical simulations. We obtain the following values for these exponents: d_f ≈ 1.5, d_w ≈ 2.4, μ^∼ ≈ 0.9. We observe that the Einstein relation holds for these structures μ^∼ ≈ −d_f + d_w. These results indicate that coastal karst networks can be considered as critical systems and this provides some foundations to model them within this framework.