This paper introduces an analyse of the fractal dimension by Richardson's method. Two different ways to calculate the fractal dimension are presented with their related calculation errors and applied the Von Koch curves. A Monte-Carlo simulation of the evolution of the grains' boundaries when heating shows that the interfaces lose their fractal characteristics as reported in experimental work. This result is interpreted by dissipation of the energy during the evolution of the grain boundary. (c) 2006 Springer Science + Business Media, Inc.