A keystone of the molecular reductionist approach to cellular biology is a specific deductive strategy relating genotype to phenotype-two distinct categories. This relationship is based on the assumption that the intermediary cellular network of actively transcribed genes and their regulatory elements is deterministic (i.e., a link between expression of a gene and a phenotypic trait can always be identified, and evolution of the network in time is predetermined). However, experimental data suggest that the relationship between genotype and phenotype is nonbijective (i.e., a gene can contribute to the emergence of more than just one phenotypic trait or a phenotypic trait can be determined by expression of several genes). This implies nonlinearity (i.e., lack of the proportional relationship between input and the outcome), complexity (i.e. emergence of the hierarchical network of multiple cross-interacting elements that is sensitive to initial conditions, possesses multiple equilibria, organizes spontaneously into different morphological patterns, and is controlled in dispersed rather than centralized manner), and quasi-determinism (i.e., coexistence of deterministic and nondeterministic events) of the network. Nonlinearity within the space of the cellular molecular events underlies the existence of a fractal structure within a number of metabolic processes, and patterns of tissue growth, which is measured experimentally as a fractal dimension. Because of its complexity, the same phenotype can be associated with a number of alternative sequences of cellular events. Moreover, the primary cause initiating phenotypic evolution of cells such as malignant transformation can be favored probabilistically, but not identified unequivocally. Thermodynamic fluctuations of energy rather than gene mutations, the material traits of the fluctuations alter both the molecular and informational structure of the network. Then, the interplay between deterministic chaos, complexity, self-organization, and natural selection drives formation of malignant phenotype. This concept offers a novel perspective for investigation of tumorigenesis without invalidating current molecular findings. The essay integrates the ideas of the sciences of complexity in a biological context.