Breast cancer is the leading cause of cancer death among women. By the following research we report on a morphological study of 30 cases as seen in mammograms, trying to discriminate among benign and malignant tumors in order to develop new tools investigation in cancer diagnosis. From the contour of each mass, we computed the fractal dimension using box-counting algorithm and for each mammogram texture we computed the lacunarity. We found that the fractal dimension value is not sufficient to differentiate among benign and malignant cases, but it was really effective when it was combined with lacunarity. In conclusion, the results obtained showed that the fractal measure is an important tool for the diagnosis of breast cancer.