MULTIFRACTALITY OF SNOWFLAKES

The results of the extensive numerical simulations of the Dielectric B reakdown Model (DBM) with noise reduction on the hexagonal lattice are presented. Seventy-five clusters grown under different boundary condi tions consisting of 16 000 particles on the lattice 1001 x 1001 were g enerated. The simulations were done for the noise reduction parameter s equal to 200 and two values of the parameter eta, namely for eta = 0 .5 and 1. For the latter case, two boundary conditions were considered : the DBM and DLA b.c. Such a growth model leads to the formation of t he fractal objects resembling real snowflakes. The growth probabilitie s were stored at the five stages of the clusters growth: at the masses of 1000, 2000, 4000, 8000 and 16 000 particles. Multifractal analysis was performed and obtained results are presented. The comparison of t wo methods: the histogram and moments methods, is provided. We discove r that for the eta = 0.5 parameter, there is a phase transition, while for eta = 1, there appears to be no phase transition. Besides the usu al growth probability measure, the measure given by the noise reductio n counters is considered and multifractality of it is presented.