We report a technique for using an evolutionary algorithm to select the parameters for a data-driven iterated function system. Such iterated function systems are typically driven with uniform random numbers to produce fractals. We instead drive the iterated function system with a biased source mimicking DNA with and without stop codons. An evolutionary algorithm is used to produce fractals that visually display the reading frame DNA. We perform a second set of experiments using the whole genome of mycobacterium tuberculosis in two different reading frames. The fractals located with our evolutionary algorithm correctly separate the DNA into in-frame and out-of-frame for the simulated data and the mycobacterium DNA. The fractals do not give dramatic visual cues to the differences for the mycobacterium data unless points associated with different members of the iterated function system are shaded. Close examination of the fractals yields insight into DNA structure.