Fluorescence photo-switching of native, unmodified DNA using visible light enables label-free, nanoscale, single-molecule photon localization microscopy (PLM) of chromatin structure. Compared with conventional label-based super resolution imaging techniques, the label-free DNA-PLM has the advantage of faithfully resolving the native nucleotides under non-perturbing conditions, thus allowing a reliable analysis of the chromatin organization. Recently, we have developed an algorithm to quantify the chromatin spatial distribution based on label-free DNA-PLM images by calculating the fractal dimension from the chromatin cluster size and the number of photon emission events. For demonstration, we employed label-free DNA-PLM with TIRF illumination, and imaged the nuclei of ovarian cancer cells with three descending chromatin heterogeneities: the P53 mutation (M248), the wild type (A2780), and the wild type treated with a commonly-used chemotherapeutic drug celecoxib (Cele). Using the algorithm, we extracted the fractal dimensions for nuclear chromatin. We found that the fractal dimension is between 2 to 3 for all cells, which lies in the range of reported values from other techniques (e.g., TEM). We also observed that M248 has the highest fractal dimension while Cele has the lowest, a perfect match with the experimental expectations. We believe this study can provide a new approach to quantify label-free super-resolution imaging of macromolecular structures and could contribute to our knowledge of native in-vitro nuclear chromatin configurations.