We investigated the structural complexity and texture of the cytoskeleton and nucleus in human mesenchymal stem cells during early phase differentiation into osteoblasts according to the differentiation–induction method: mechanical and/or chemical stimuli. For this, fractal dimension and a number of parameters utilizing the gray-level co-occurrence matrix (GLCM) were calculated based on single-cell images after confirmation of differentiation by immunofluorescence staining. The F-actin and nuclear fractal dimensions were greater in both stimulus groups compared with the control group. The GLCM values for energy and homogeneity were lower in fibers of the F-actin cytoskeleton, indicating a dispersed F-actin arrangement during differentiation. In the nuclei of both stimulus groups, higher values for energy and homogeneity were calculated, indicating that the chromatin arrangement was chaotic during the early phase of differentiation. It was shown and confirmed that combined stimulation with mechanical and chemical factors accelerated differentiation, even in the early phase. Fractal dimension analysis and GLCM methods have the potential to provide a framework for further investigation of stem cell differentiation.