A model of an avascular tumor growth that considers the basic biological principles of cell proliferation, motility, dead and genes mutations is proposed and analyzed. The  tumor microenvironment is incorporated by assuming that nutrients spatial gradients influence cancer cell metabolism and thus the probability of acquiring mutations. A set of six genes was identified from a regulatory network analysis which is believed to play an important role in tumor growth. Gene mutation dynamics was described as a stochastic process that is coupled to nutrients transport equations. For each representative tumor its diversity, represented by the Shannon index, and its spatial heterogeneity, measured by its fractal dimension were calculated. These quantities are important in the clinical diagnosis of tumor malignancy. A tumor malignancy diagram, obtained by plotting diversity versus fractal dimension, was calculated for different values of a parameter β, that modulates proliferation rate due to the occurrence of mutations. It is found that, when β < 1, tumors show greater diversity and more spatial heterogeneity as compared with β > 1. More importantly, it is found that the results and conclusions are similar when we use the six-gene set versus a sixteen-gene set.