Multifractal Distribution of Dendrite on One-dimensional Support

Abstract

We apply multifractal analysis to an experimentally obtained quasi-two-dimensional crystal with fourfold symmetry, in order to characterize the sidebranch structure of a dendritic pattern. In our analysis, the stem of the dendritic pattern is regarded as a one-dimensional support on which a measure is defined and the measure is identified with the area, perimeter length, and growth rate distributions. It is found that these distributions have multifractality and the results for the area and perimeter length distributions, in the competitive growth regime of sidebranches, are phenomenologically understood as a simple partitioning process.