Evolutionary algorithms are used to evolve Self-Driving Automata (SDAs), finite automata that both read and output symbols. The output of the SDA can be used to generate biological data in the form of sequences or networks. The fitness of an SDA is assessed based on its ability to match real target data: DNA sequences and weighted contact networks. In sequence matching, the SDA method achieves 96.5% accuracy for one of the sequences, and over 90% for half of the target sequences, which range in length from 57 to 102 bases. In network matching, the SDA method is compared to another well-known method using three fitness functions. While the SDA method successfully reproduces multiple clusters in the target network, in general the results lag behind the comparator method. Several avenues for future work are identified, with the eventual goal of using SDAs to identify patterns in biological sequence data.