Templated self-assembly of block copolymer thin films can generate periodic arrays of microdomains within a sparse template, or complex patterns using 1:1 templates [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] . However, arbitrary pattern generation directed by sparse templates remains elusive. Here, we show that an array of carefully spaced and shaped posts, prepared by electron-beam patterning of an inorganic resist, can be used to template complex patterns in a cylindrical-morphology block copolymer. We use two distinct methods: making the post spacing commensurate with the equilibrium periodicity of the polymer, which controls the orientation of the linear features, and making local changes to the shape or distribution of the posts, which direct the formation of bends, junctions and other aperiodic features in specific locations. The first of these methods permits linear patterns to be directed by a sparse template that occupies only a few percent of the area of the final self-assembled pattern, while the second method can be used to selectively and locally template complex linear patterns.Microphase separation of a block copolymer thin film can generate dense arrays of microdomains with periodicity as low as $10 nm (refs 6,16-19). Such arrays have been used as lithographic masks to pattern various functional materials, and to create devices including nanocrystal flash memory, nanowire transistors, gas sensors and patterned magnetic recording media [20][21][22][23][24][25] . Block copolymer thin film self-assembly on an unpatterned substrate leads to close-packed arrays of features such as lines or dots that lack long-range order, thus limiting their utility. As a result, both chemical and topographical substrate features have been used to template or guide block copolymer self-assembly, imposing long-range order and generating microdomain geometries not observed in untemplated films [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] . These templates are often defined using electronbeam lithography (EBL) [3][4][5]7,8,11 , because of its ability to pattern small features of arbitrary geometry. However, the serial nature of EBL makes it clearly advantageous to minimize the density of the EBL-written features required to template a given arrangement of block copolymer microdomains. Even in a production context in which EBL is used only to write a master pattern that is to be replicated by some higher-throughput mechanism (such as nanoimprinting), the time required just to write the master can be prohibitively long. The challenge in template design is therefore to find a set of template features of minimum complexity that will deterministically program the block copolymer to form a desired final pattern, such as an interconnect level in an integrated circuit, which may contain both periodic and aperiodic features.We describe an approach to this problem that uses a sparse array of chemically functionalized topographical posts to control the self-assembly of dense linear block copolymer (BCP) stru...