This PhD work is devoted to developing an experimental framework to investigate chemical spatiotemporal organization through mechanisms that could be at play during pattern formation in development. We introduce new tools to increase the versatility of DNA-based networks as pattern-forming systems. The emergence of organization in living systems is a longstanding fundamental question in biology. The two most influential ideas in developmental biology used to explain chemical pattern formation are Wolpert's positional information and Turing's reaction-diffusion self-organization. In the case of positional information, the pattern emerges from a pre-existing morphogen gradient across space that provides positional values as in a coordinate system. Whereas, the Turing mechanism relies on self-organization by driving a system of an initially homogeneous distribution of chemicals into an inhomogeneous pattern of concentration by a process that involves solely reaction and diffusion. Although numerical simulations and mathematical analysis corroborate the incredible potential of reaction-diffusion mechanisms to generate patterns, their experimental implementation is not trivial. And despite of the exceptional achievements in pattern formation with Belousov–Zhabotinsky systems, these are difficult to engineer, thus limiting their experimental implementation to few available mechanisms. In order to engineer reaction-diffusion systems that display spatiotemporal dynamics the following three key elements must be controlled: (i) the topology of the network (how reactions are linked to each other, i.e. in a positive or negative feedback manner), (ii) the reaction rates and (iii) the diffusion coefficients. Recently, using nucleic acids as a substrate to make programmable dynamic chemical systems together with the lessons from synthetic biology and DNA nanotechnology has appeared as an attractive approach due to the simplicity to control reaction rates and network topology by the sequence. Our experimental framework is based on the PEN-DNA toolbox, which involves DNA hybridization and enzymatic reactions that can be maintained out of equilibrium in a closed system for long periods of time. The programmability and biocompatibility of the PEN-DNA toolbox open new perspectives for the engineering of the reaction-diffusion chemical synthesis, in particular in two directions. Firstly, to study biologically-inspired pattern-forming mechanisms in simplified, yet relevant, experimental conditions. Secondly to build new materials that would self-build by a process inspired from embryo morphogenesis. We worked towards the goal of meeting the two requirements of Turing patterning, transferring chemical spatiotemporal behavior into material patterns, and imposing boundary conditions to spatiotemporal patterns. Therefore, the structure of this document is divided into four specific objectives resulting in four chapters. In chapter 1 we worked on testing a DNA-based reaction network with an inhibitor-activator topology. In chapter 2 we focused on developing a strategy to tune the diffusion coefficient of activator DNA strands. In chapter 3 we explored how chemical patterns determine the shape of a material. Finally, in chapter 4 we addressed the issue of controlling the geometry over a DNA-based reaction-diffusion system. Overall, we have expanded the number of available tools to study chemical and material pattern formation and advance towards Turing patterns with DNA.