Cellular information dynamics during somatic evolution of the malignant phenotypes are complex and poorly understood. Accumulating, random genetic mutations and, therefore, loss of genomic information appears necessary for carcinogenesis. However, additional control parameters can be inferred because unconstrained mutagenesis would ultimately produce cellular information degradation incompatible with life. Similarly, the stability of some genomic segments, such as those controlling proliferation and metabolism, indicates the presence of selective mutational constraints. By applying Information Theory and Extreme Physical Information (EPI) analysis, we demonstrate that the phenotypic characteristics and growth pattern of cancer populations are emergent properties resulting from the nonlinear dynamics of accumulating, random genetic mutations and tissue selection factors. Maximum quantitative loss of transgenerational information is demonstrated in genomic segments encoding negative or neutral evolutionary properties. This is most evident in the progressive dedifferentiation observed during carcinogenesis and may terminate in a differentiation "information catastrophe" producing decoherent cellular morphology and function. In contrast, microenvironmental selection pressures preserve genomic information controlling properties that confer selective growth advantages even in the presence of a high background mutation rate. Thus, phenotypic traits characteristically retained by tumor populations can be identified as critical selection parameters favoring clonal proliferation. The information model of carcinogenesis is tested by applying EPI analysis to predict tumor growth dynamics. We found that cellular proliferation attributable to information degradation will produce power law tumor growth with an exponent of 1.62. Data from six published studies that use sequential mammograms to measure the volume of small, untreated human breast cancers demonstrate power law tumor growth with a mean exponent value of 1.73 +/- 0.23. Other predictions including exponential growth of tumor cells in vitro are also supported by experimental observations. The nonlinear dynamics of stochastic information loss constrained by somatic evolution indicate that carcinogenesis will not be associated with any predictable, fixed sequence of genomic alterations. Rather, sporadic clinical cancers are emergent structures produced by multiple, fundamentally nondeterministic genetic pathways.