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In this paper we investigate the computational power of the polygonal tileassembly model (polygonal TAM) at temperature 1, i.e. in non-cooperativesystems. The polygonal TAM is an extension of Winfree's abstract tile assemblymodel (aTAM) which not only allows for square tiles (as in the aTAM) but alsoallows for tile shapes that are polygons. Although a number of self-assemblyresults have shown computational universality at temperature 1, these are thefirst results to do so by fundamentally relying on tile placements incontinuous, rather than discrete, space. With the square tiles of the aTAM, itis conjectured that the class of temperature 1 systems is not computationallyuniversal. Here we show that the class of systems whose tiles are composed of aregular polygon P with n > 6 sides is computationally universal. On the otherhand, we show that the class of systems whose tiles consist of a regularpolygon 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-regularpolygon with n >= 3 sides are computationally universal.

Computing in continuous space with self-assembling polygonal tiles