Using meta-analyses, we introduce a unicellular attractor (UCA) model integrating essential features of the ‘atavistic reversal’, ‘cancer attractor’, ‘somatic mutation’, ‘genome chaos’, and ‘tissue organization field’ theories. The ‘atavistic reversal’ theory is taken as a keystone. We propose a possible mechanism of this reversal, its refinement called ‘gradual atavism’, and evidence for the ‘serial atavism’ model. We showed the gradual core-to-periphery evolutionary growth of the human interactome resulting in the higher protein interaction density and global interactome centrality in the UC center. In addition, we revealed that UC genes are more actively expressed even in normal cells. The modeling of random walk along protein interaction trajectories demonstrated that random alterations in cellular networks, caused by genetic and epigenetic changes, can result in a further gradual activation of the UC center. These changes can be induced and accelerated by cellular stress that additionally activates UC genes (especially during cell proliferation), because the genes involved in cellular stress response and cell cycle are mostly of UC origin. The functional enrichment analysis showed that cancer cells demonstrate the hyperactivation of energetics and the suppression of multicellular genes involved in communication with the extracellular environment (especially immune surveillance). Collectively, these events can unleash selfish cell behavior aimed at survival at all means. All these changes are boosted by polyploidization. The UCA model may facilitate an understanding of oncogenesis and promote the development of therapeutic strategies.