Maximal homology alignment is a new biologically-relevant approach to DNA sequence alignment that embraces microparalogy. It departs from the current method of gapped alignment, which uses a simple, binary state model of nucleotide position. In gapped alignment nucleotide positions have either no relationship (1-to-None) or else orthological relationship (1-to-1) with nucleotides in other sequences. Maximal homology alignment, however, allows additional states such as 1-to-Many and Many-to-Many, thus modeling both orthological and paralogical relationships, which together comprise the main homology types. Maximal homology alignment collects dispersed microparalogy into the same alignment columns on multiple rows, and thereby generates a two-dimensional representation of a single sequence. Sequence alignment then proceeds as the alignment of two-dimensional topological objects. The operations of producing and aligning two dimensional auto-alignments motivate a need for tests of two dimensional homological integrity that are both necessary and sufficient. Here, I work out and implement basic principles for computationally handling the two dimensions of positional homology, which are inherent to biological sequences due to replication slippage and related errors. I then show that maximal homology alignment is more suited and more informative than gapped alignment for modeling the evolution of genetic sequences, which harbor large numbers of small insertions and deletions originating as local microparalogy. These results show that both conserved and non-conserved genomic sequences are imbued with a signature of replication slippage that is absent from their random permutations. KEYWORDS dimensionality; DNA microfoam; Drosophila; enhancer DNAs; gapped alignment (GA); maximal homology alignment (MHA); positional homology; replication slippage; tandem repeats S equences of covalently-linked nucleotides and their evolutionary relationships are the basis of gene homology. The smallest possible scale to ascribe such homology is that of individual nucleotide positions ("site positional homology"). Of course this is possible only in the context of homological inference based on multiple nucleotide positions in a sequence.By studying the function and evolution of regulatory DNA sequences (transcriptional enhancers in Ciona and Drosophila), which are not constrained by rigid, protein-coding, triplet reading frames (Erives et al. Brittain et al. 2014;Stroebele and Erives 2016), I conclude that site positional homology is incorrectly handled by gapped alignment (GA). GA was originally adopted by necessity in order to compare protein sequences of divergent lengths (Braunitzer's gappy comparisons of α-and β-hemoglobin