Genomic signatures are important as a source of comparison and classification of genomes. In particular, the Chaos Game Representation, an iterative mapping method, generates a frequency distribution of nucleotides of length k and represents it on a lattice of size 2 k x2 k . However, it lacks continuity in the sense that very different sequences are represented on contiguous cells of the lattice. Here, we propose an alternative method that organizes cells in such a way that continuity is higher than in the Chaos Game Rrepresentations. The cell organization is the outcome of a Self-Organizing Map and the obtained frequency distribution is named Self-Organized Chaos Game Representation. Experiments show that this visualization method is, at least, as good as the Chaos Game Representation, but it gives it a more intuitive sense when interpreting the images.