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We analyzed a quantitative multiscale model that describes the epigenetic dynamics during the growth and evolution of an avascular tumor. A gene regulatory network (GRN) formed by a set of ten genes that are believed to play an important role in breast cancer development was kinetically coupled to the microenvironmental agents: glucose, estrogens, and oxygen. The dynamics of spontaneous mutations was described by a Yule-Furry master equation whose solution represents the probability that a given cell in the tissue undergoes a certain number of mutations at a given time. We assumed that the mutation rate is modified by a spatial gradient of nutrients. The tumor mass was simulated by means of cellular automata supplemented with a set of reaction diffusion equations that described the transport of microenvironmental agents. By analyzing the epigenetic state space described by the GRN dynamics, we found three attractors that were identified with cellular epigenetic states: normal, precancer and cancer. For two-dimensional (2D) and three-dimensional (3D) tumors we calculated the spatial distribution of the following quantities: (i) number of mutations, (ii) mutation of each gene and, (iii) phenotypes. Using estrogen as the principal microenvironmental agent that regulates cells proliferation process, we obtained tumor shapes for different values of estrogen consumption and supply rates. It was found that he majority of mutations occurred in cells that were located close to the 2D tumor perimeter or close to the 3D tumor surface. Also, it was found that the occurrence of different phenotypes in the tumor are controlled by estrogen concentration levels since they can change the individual cell threshold and gene expression levels. All results were consistently observed for 2D and 3D tumors. Author summary: We introduce and analyze in detail a 2D and 3D quantitative multiscale model that describes the growth and epigenetic evolution of an avascular breast tumor. We obtain series of microarrays that describe the activation/inhibit levels of a group of genes that respond to the occurrence of oxygen and estrogen concentration gradients. We identify three cell phenotypes: normal, precancer and cancer, that are crucial to understand the tumor structure, the spatial distribution of mutations and the tumor heterogeneity. Finally, we found that the estrogen concentration gradients are related to the variation of gene expression levels and phenotypes occurrence. These findings strongly suggest that it is possible to develop epigenetic cancer treatment alternatives to either stop or reverse tumor evolution. [ABSTRACT FROM AUTHOR]