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Additive manufacturing enables the generation of 3D structures with predefined shapes from a wide range of printable materials. However, most of the materials employed so far are static and do not provide any intrinsic programmability or pattern-forming capability. Here, a low-cost 3D bioprinting approach is developed, which is based on a commercially available extrusion printer that utilizes a DNA-functionalized bioink, which allows to combine concepts developed in dynamic DNA nanotechnology with additive patterning techniques. Hybridization between diffusing DNA signal strands and immobilized anchor strands can be used to tune diffusion properties of the signals, or to localize DNA strands within the gel in a sequence-programmable manner. Furthermore, strand displacement mechanisms can be used to direct simple pattern formation processes and to control the availability of DNA sequences at specific locations. To support printing of DNA-functionalized gel voxels at arbitrary positions, an open source python script that generates machine-readable code (GCODE) from simple vector graphics input is developed.