A new method to calculate the fractal dimension of an interface application to a Monte Carlo diffusion process

A new method to calculate the fractal dimension called Slit island average normalised autocorrelation method is proposed and validated on deterministic and stochastic fractal curves. This method well estimates the fractal dimension and does not require self affinity or self similarity of the surface or the interface. Then fractal grains are constructed by an iteration function system (IFS) method and a simulation of grain growth is carried out by the Monte Carlo method. It is shown that the fractal dimension of the grain boundaries decreases with the annealing time and follows a sigmoidal equation that converges to unity.