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Recent studies on the geometry of fractals indicate that tumors with irregular shapes can be utilized for the study of the morphology and diagnosis of cancerous cases. In this paper, we deal with the fractal modeling of the mammographic images and their background morphology. It is shown that the use of fractal modeling as applied to a given image can clearly discern cancerous zones from noncancerous areas. Our results show that fractal modeling of images can be used as an effective tool for identification of cancerous cells. For fractal modeling, the original image is first segmented into appropriate fractal boxes followed by identifying the fractal dimension of each windowed section. We have used two dimensional box counting algorithm after which based on the order of the computations, they are placed in an appropriate matrix to facilitate the required computations. Finally using eight features identified as characteristic features of tumors extracted from mammogram images, the results obtained from the preliminary analysis stages, were utilized in a neural network for classification of cells into malignant and benign with the accuracy of 89.21% classification results.