Fractals are useful for conveying multiple types of information with shape and color in a single picture. We report on a standard technique for visualizing DNA or other sequence data with a fractal algorithm and then twice generalize the technique to obtain two types of evolvable fractals. Both are forms of iterated function systems(IFS), collections of randomly driven or data driven contraction maps. The first, an indexed IFS, uses incoming data to choose which contraction map will be applied next. The second, called a chaos automata, drives a finite state machine with incoming sequence data and associates a contraction map with each state. Both evolvable fractals are tested on their ability to separate DNA from distinct microbial genomes. Design of fitness function is a critical issue as we are trying to create fractals that look good and convey information about the sequences driving them. It is demonstrated that chaos automata are superior to the indexed IFS on the test problem. Potential improvements in the fractal chromosomes, fitness functions, and issues to be resolved to obtain useful applications are discussed.