  We show that the Tile Assembly Model exhibits a strong notion of universality
where the goal is to give a single tile assembly system that simulates the
behavior of any other tile assembly system. We give a tile assembly system that
is capable of simulating a very wide class of tile systems, including itself.
Specifically, we give a tile set that simulates the assembly of any tile
assembly system in a class of systems that we call \emph{locally consistent}:
each tile binds with exactly the strength needed to stay attached, and that
there are no glue mismatches between tiles in any produced assembly.
  Our construction is reminiscent of the studies of \emph{intrinsic
universality} of cellular automata by Ollinger and others, in the sense that
our simulation of a tile system $T$ by a tile system $U$ represents each tile
in an assembly produced by $T$ by a $c \times c$ block of tiles in $U$, where
$c$ is a constant depending on $T$ but not on the size of the assembly $T$
produces (which may in fact be infinite). Also, our construction improves on
earlier simulations of tile assembly systems by other tile assembly systems (in
particular, those of Soloveichik and Winfree, and of Demaine et al.) in that we
simulate the actual process of self-assembly, not just the end result, as in
Soloveichik and Winfree's construction, and we do not discriminate against
infinite structures. Both previous results simulate only temperature 1 systems,
whereas our construction simulates tile assembly systems operating at
temperature 2.
