The current prognostic parameters, including tumor volume, biochemistry, or immunohistochemistry, are not sufficient to reflect the properties of cancer cells that distinguish them from normal cells. Our focus is to evaluate the effects of a combination of microtubule-polymerizing Taxol and -depolymerizing colchicine on IAR20 PC1 liver cells by measuring the surface fractal dimension as a descriptor of two-dimensional vascular geometrical complexity. The fractal dimension offers a rapid means of assessing cell shape. Furthermore, we show correlations of fractal dimensions of cell contours with the latent factors from our previously employed cell shape analysis.