Self-assembly has been employed in nano-technology to build crystals using individual components (commonly referred to as tiles) with limited control. Templates of regular lattice structures for two-dimensional scaffolds and interconnects have been recently implemented by self-assembly. This study proposes a diagonally based growth scheme that is applicable to these templates of interconnects (as an example). Differently from previous techniques (mostly sequential in execution), growth is allowed along two different directions in the aggregate, thus permitting a parallel mode of operation. This is made possible by utilising a tile set and binding scheme to allow multiple seed tiles to grow along the main diagonal of the pattern. The conditions by which this type of new growth is possible at a reduced error occurrence in mismatched tiles, are presented; error tolerance is achieved by employing healing and so-called robust generation of the seed tiles, thus ensuring that pattern growth is controlled along both directions. Simulation results are presented under different scenarios of growth direction (inclusive of backward growth for healing).