Heterochromatin represents 30% of eukaryotic genome in Drosophila and 15% in humans. Despite extensive research spanning many decades, its evolutionary significance, as well as the forces that guarantee its maintenance, are still elusive. Many theoretical and experimental approaches have led researchers to propose several conceptual frameworks to elucidate the nature of this huge mysterious genetic material and its spreading in all eukaryotic genomes. "Junk DNA" as well as "selfish genetic material" are two examples of such attempts, but several lines of evidence suggest that such explanations are incomplete. In fact, if the selfish DNA hypothesis does not explain the mapping of genetic functions in heterochromatin, then the junk DNA hypothesis is incomplete in describing both emergence of genetic functions and their maintenance in the eukaryotic heterochromatin. Recent developments in the physics of complex systems and mathematical concepts such as fractals provide new conceptual clues to answer several basic questions concerning the emergence of heterochromatin in eukaryotic genomes, its evolutionary significance, the forces that guarantee its maintenance, and its peculiar behavior in the eukaryotic cell. The aim of this paper is to provide a new theoretical framework for the heterochromatin, considering such genetic material in physical terms as a complex adaptive system. We apply some computer calculations to demonstrate the nonlinearity of the flux of genetic information along the phylogenic tree. Fractal dimensions of representative heterochromatic sequences are provided. A theory is proposed in which heterochromatin is considered a system that evolves in a self-organized manner at the edge of cellular and environmental chaos.