The late Professor J.S. Nicolis always emphasized, both in his writings and in presentations and discussions with students and friends, the relevance of a dynamical systems approach to biology. In particular, viewing the genome as a "biological text" captures the dynamical character of both the evolution and function of the organisms in the form of correlations indicating the presence of a long-range order. This genomic structure can be expressed in forms reminiscent of natural languages and several temporal and spatial traces left by the functioning of dynamical systems: Zipf laws, self-similarity and fractality. Here we review several works of our group and recent unpublished results, focusing on the chromosomal distribution of biologically active genomic components: Genes and protein-coding segments, CpG islands, transposable elements belonging to all major classes and several types of conserved non-coding genomic elements. We report the systematic appearance of power-laws in the size distribution of the distances between elements belonging to each of these types of functional genomic elements. Moreover, fractality is also found in several cases, using box-counting and entropic scaling. We present here, for the first time in a unified way, an aggregative model of the genomic dynamics which can explain the observed patterns on Chaos, Information Processing and Paradoxical Games Downloaded from www.worldscientific.com by MONASH UNIVERSITY on 02/02/15. For personal use only. 222 D. Polychronopoulos et al.the grounds of known phenomena accompanying genome evolution. Our results comply with recent findings about a "fractal globule" geometry of chromatin in the eukaryotic nucleus.