Complex, self-assembling, two-dimensional nanostructures can be built of single-stranded DNA tiles by a method that allows individual control of more than one thousand distinct components. Programmed DNA self-assembly is widely used to create nanometre-sized structures. Modular strategies promise simplicity and versatility, yet cannot easily assemble large numbers of small strands into prescribed and complex shapes. Peng Yin and colleagues overcome this problem by designing a molecular canvas: a rectangle assembled from single-stranded tiles each consisting of a short and unique 42-base DNA strand that folds into a 3-nanometre-by-7-nanometre tile and attaches to 4 neighbouring tiles. A desired shape, drawn on the canvas, is produced by simply mixing those strands that correspond to pixels covered by the target shape, and excluding 'off'-pixel strands. With a master strand collection for a 310-pixel canvas, the team then creates more than 100 distinct and complex two-dimensional shapes that establish the method as a simple, modular and robust framework for assembling short synthetic DNA strands into complex DNA nanostructures. Programmed self-assembly of strands of nucleic acid has proved highly effective for creating a wide range of structures with desired shapes1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25. A particularly successful implementation is DNA origami, in which a long scaffold strand is folded by hundreds of short auxiliary strands into a complex shape9,14,15,16,18,19,20,21,25. Modular strategies are in principle simpler and more versatile and have been used to assemble DNA2,3,4,5,8,10,11,12,13,17,23 or RNA7,22 tiles into periodic3,4,7,22 and algorithmic5 two-dimensional lattices, extended ribbons10,12 and tubes4,12,13, three-dimensional crystals17, polyhedra11 and simple finite two-dimensional shapes7,8. But creating finite yet complex shapes from a large number of uniquely addressable tiles remains challenging. Here we solve this problem with the simplest tile form, a ‘single-stranded tile’ (SST) that consists of a 42-base strand of DNA composed entirely of concatenated sticky ends and that binds to four local neighbours during self-assembly12. Although ribbons and tubes with controlled circumferences12 have been created using the SST approach, we extend it to assemble complex two-dimensional shapes and tubes from hundreds (in some cases more than one thousand) distinct tiles. Our main design feature is a self-assembled rectangle that serves as a molecular canvas, with each of its constituent SST strands—folded into a 3 nm-by-7 nm tile and attached to four neighbouring tiles—acting as a pixel. A desired shape, drawn on the canvas, is then produced by one-pot annealing of all those strands that correspond to pixels covered by the target shape; the remaining strands are excluded. We implement the strategy with a master strand collection that corresponds to a 310-pixel canvas, and then use appropriate strand subsets to construct 107 distinct and complex two-dimensional shapes, thereby establishing SST assembly as a simple, modular and robust framework for constructing nanostructures with prescribed shapes from short synthetic DNA strands.