Fractal Description of a Growing Dendritic Structure

In this paper in terms of random fractal the description of a growing random fractal is proposed. The refined relations describing the fractal dimension of a random fractal and the volume occupied by a dendritic particle in $d$-dimensional topological space are established. Moreover, the established relations are derived for an arbitrary form of elementary fractal fragments which fit dendritic branches. The calculation results for the parabolic form of the fragment of an elementary fractal which grows with time are given.