The organization of the nucleosome array is a critical component of chromatin assembly as well as its function. Here we investigated the contribution of DNA sequence and internucleosomal interactions to the organization of nucleosomal arrays using Atomic Force Microscopy. We assembled nucleosomes on DNA substrates allowing for the formation of tetranucleosomes. We found that nucleosomes are capable of forming constructs with no discernible space between them, even in the case of dinucleosomes. Simulated assembly of tetranucleosomes by random placement revealed that array compaction is promoted by internucleosomal interactions. We developed a theoretical model to account for the role of DNA sequence and internucleosomal interactions in the formation of nucleosome structures. These findings suggest that the affinity of nucleosomes to the DNA sequence and the strengths of internucleosomal interactions are the two major factors defining the compactness of chromatin.