Scaling Behaviors of Multifractals in Two-dimensional Structures

Abstract

We find that the baduk game can be described in terms of multifractals via a generalized dimension and a scaling exponent. For our case, the generalized dimension and scaling exponent can be estimated numerically from the black and mixed (black and white) stones provided the area form of the baduk game in which we assume that the structure is presented in terms of the self-similar structure. We particularly find that the fractal dimension has a much larger value and that the dynamical behavior becomes much more chaotic, as the area increases.