Before revision:  It is shown that a chaotic (deterministic) order, rather than a stochastic randomness, controls the energy minima positions of the staking interactions in the DNA sequences .
After revision:  It is shown , in particular, that the nucleotide sequences in DNA molecules have robust cluster-scaling properties. These properties are relevant to both types of nucleotide pair-bases interactions: hydrogen bonds and stacking interactions. It is shown that taking into account the cluster-scaling properties can help to improve heterogeneous models of the DNA dynamics. It is also shown that a chaotic (deterministic) order, rather than a stochastic randomness, controls the energy minima positions of the staking interactions in the DNA sequences .