Strict self-assembly of discrete self-similar fractals

Strict Self-Assembly of Discrete Self-Similar Fractals

Discrete self-similar fractals are infinite aperiodic shapes that have received much interest in the domain of tile self-assembly. For instance, in it was shown that the infinite Sierpinski triangle cannot strictly self-assemble in the aTAM, but a fibered approximation can be. In it was shown that additional DSSFs cannot strictly self-assemble in the aTAM, but their fibered approximations can. Just a few of the additional results related to DSSFs, including more impossibility results, other approximations, and strict self-assembly in other models can be found in .

While in it was conjectured that no DSSF can strictly self-assemble in the aTAM, that conjecture has been proven false. In fact, two different methods have been demonstrated for developing aTAM systems that strictly self-assemble DSSFs, and the following two sections give overviews of each.

DSSFs via Self-describing circuits

TODO: describe the work by Florent Becker in

DSSFs via Quines

TODO: describe the work by Hader and Patitz, in progress...