A 3D chaos game is shown to be a useful way for encoding DNA sequences. Since matching subsequences in DNA converge in space in 3D chaos game encoding, a DNA sequence’s 3D chaos game representation can be used to compare DNA sequences without prior alignment and without truncating or padding any of the sequences. Four methods inspired by shape-similarity comparison techniques show that this form of encoding can perform as well as alignment-based techniques for building phylogenetic trees. The first method uses the volume overlap of intersecting spheres and the remaining three use shape signatures in the 3D chaos game trajectory: edge length in a 3-point sliding window, angles in a 3-point sliding window, and coordinates of the chaos-game trajectory. The methods are tested using: 1) mitochondrial DNA from four groups of primates, 2) the first exon of the beta-globin gene for 11 species, and 3) set of simulated DNA sequences. Simulations show that methods produce distances that are, on average, agnostic regarding whether mutations are deletions or substitutions.