  We show the first asymptotically efficient constructions in the so-called
"noncooperative planar tile assembly" model.
  Algorithmic self-assembly is the study of the local, distributed,
asynchronous algorithms ran by molecules to self-organise, in particular during
crystal growth. The general cooperative model, also called "temperature 2",
uses synchronisation to simulate Turing machines, build shapes using the
smallest possible amount of tile types, and other algorithmic tasks. However,
in the non-cooperative ("temperature 1") model, the growth process is entirely
asynchronous, and mostly relies on geometry. Even though the model looks like a
generalisation of finite automata to two dimensions, its 3D generalisation is
capable of performing arbitrary (Turing) computation, and of universal
simulations, whereby a single 3D non-cooperative tileset can simulate the
dynamics of all possible 3D non-cooperative systems, up to a constant scaling
factor.
  However, it was shown that the original 2D non-cooperative model is not
capable of universal simulations, and the question of its computational power
is still widely open. Here, we show an unexpected result, namely that this
model can reliably grow assemblies of size Omega(n log n) with only n tile
types, which is the first asymptotically efficient positive construction.
