  We present a simple route to circumvent kinetic traps which affect many types
of DNA nanostructures in their self-assembly process. Using this method, a new
2D DNA lattice made up of short, single-stranded tile (SST) motifs was created.
Previously, the growth of SST DNA assemblies was restricted to 1D (tubes and
ribbons) or finite-sized 2D (molecular canvases). By utilizing the
substrate-assisted growth method, sets of SSTs were designed as unit cells to
self-assemble into periodic and aperiodic 2D lattices which continuously grow
both along and orthogonal to the helical axis. Notably, large-scale ($\sim 1$
$\mu$m$^2$) fully periodic 2D lattices were fabricated using a minimum of just
2 strand species. Furthermore, the ability to create 2D lattices from a few
motifs enables certain rules to be encoded into these SSTs to carry out
algorithmic self-assembly. A set of these motifs were designed to execute
simple 1-input 1-output COPY and NOT algorithms, the space-time manifestations
which were aperiodic 2D algorithmic SST lattices. The methodology presented
here can be straightforwardly applied to other motifs which fall into this type
of kinetic trap to create novel DNA crystals.
