Biological and biochemical systems are manifestations of chemical reaction networks (CRNs). The ability to design and engineer such networks may allow the construction of artificial systems that are as complex as those seen in biology, opening the way to translational possibilities including adaptive materials. One venue for progress is the design of autonomous systems capable of pattern generation; however many synthetic CRNs, such as the Belousov-Zhabotinsky reaction, cannot be rewired to encode more complex interactions and thus lack the capacity for more detailed engineering algorithms. In contrast, DNA is an information-rich molecule with predictable and reliable base-pairing interactions and well-studied kinetics, and the use of DNA has greatly enabled the rational design of much more complex synthetic CRNs. Recent advances in the DNA computing field include circuits for pattern transformation, an example of self-organization. An arsenal of tools for designing DNA circuits to implement various CRNs has been developed by DNA nanotechnologists, including software to reliably program strand-displacement nucleic acid circuits. In addition, DNA walkers can be used to create CRNs with controlled diffusivity, while DNA gels similarly represent a new medium for implementing CRNs that may ultimately lead to the development of smart materials. As we will argue, future endeavors in nucleic acid-based pattern generation will be most greatly advanced by harnessing well-known enzymatic processes to serve as generators and amplifiers. Once nucleic acid computing tools are further developed to expedite the design process of pattern generation, we anticipate a transition from proof-of-concept curiosities to application-driven inquiries.