We present a box counting fractal dimension (FD) analysis of the dendritic patterns obtained under conditions far from equilibrium via rapid evaporation of a sessile drop containing reactive ZnO nanoparticles. These dendrites were manifestations of solidified Benard-Marangoni (BM) instability convection cells, and we previously noted that their complex hierarchical morphologies were superficially analogous to the foliage of red algae, Spanish dagger, or spider plant. The fractal dimension of the Benard-Marangoni dendrites was found to vary in the range of 1.77-1.89 and also depend on the size of the Benard-Marangoni cells. These fractal dimension results were correlated with the morphological details of the Benard-Marangoni cells and ZnO particle characteristics, providing a quantitative description of such complex surface patterns emerging from the dynamic process of the Benard-Marangoni instability. (C) 2018 Elsevier Inc. All rights reserved.