Studies on Random Fractal and Multifractal Structures in Korean Topography

한국지형에서의 랜덤 프랙탈과 멀티프랙탈구조의 연구

In Korean topography the behaviors of random fractals and multifractality are analytically and numerically studied on the mountain heights shown between $128{\sim}129^{\circ}E$ and $37{\sim}38^{\circ}N$. The phase transitions on the fractal structure are approximately found at the critical length $N_c=2000m$ from the values of standard deviations that it varies with both the longitudinal and latitudinal lengths. In the multifractal structure we assume that the mountain heights divided by the intervals of 20 m are located on the horizontal plane in two dimensional square lattice, and estimate the values of the generalized dimension and the scaling exponents by using the the box counting method for the three cases of square area ($1{\times}1km^2$, $2{\times}2km^2$, $4{\times}4km^2$).