Given its highly predictable self-assembly properties, DNA has proven to be an excellent template toward the design of functional materials. Prominent examples include the remarkable complexity provided by DNA origami and single-stranded tile (SST) assemblies, which require hundreds of unique component strands. However, in many cases, the majority of the DNA assembly is purely structural, and only a small "working area" needs to be aperiodic. On the other hand, extended lattices formed by DNA tile motifs require only a few strands; but they suffer from lack of size control and limited periodic patterning. To overcome these limitations, we adopt a templation strategy, where an input strand of DNA dictates the size and patterning of resultant DNA tile structures. To prepare these templating input strands, a sequential growth technique developed in our lab is used, whereby extended DNA strands of defined sequence and length may be generated simply by controlling their order of addition. With these, we demonstrate the periodic patterning of size-controlled double-crossover (DX) and triple-crossover (TX) tile structures, as well as intentionally designed aperiodicity of a DX tile structure. As such, we are able to prepare size-controlled DNA structures featuring aperiodicity only where necessary with exceptional economy and efficiency.