  In this paper we investigate the computational power of the polygonal tile
assembly model (polygonal TAM) at temperature 1, i.e. in non-cooperative
systems. The polygonal TAM is an extension of Winfree's abstract tile assembly
model (aTAM) which not only allows for square tiles (as in the aTAM) but also
allows for tile shapes that are polygons. Although a number of self-assembly
results have shown computational universality at temperature 1, these are the
first results to do so by fundamentally relying on tile placements in
continuous, rather than discrete, space. With the square tiles of the aTAM, it
is conjectured that the class of temperature 1 systems is not computationally
universal. Here we show that the class of systems whose tiles are composed of a
regular polygon P with n > 6 sides is computationally universal. On the other
hand, we show that the class of systems whose tiles consist of a regular
polygon P with n <= 6 cannot compute using any known techniques. In addition,
we show a number of classes of systems whose tiles consist of a non-regular
polygon with n >= 3 sides are computationally universal.
