Self-assembly of Self-similar Structures by Active Tiles

The natural capacity of DNA for molecular self-assembly has already been exploited to create DNA based tiles which can self-assemble into nano-scale arrays and carry out nano-scale computation. Thus far, however, all such self-assembly has been passive, in the sense that the binding capacities of a tile are never altered throughout the assembly. The idea of active tiles, tiles that can send signals to each other and activate latent binding sites, has been proposed but never incorporated into a formal model. Here, I present an extension of the existent abstract tile assembly model by defining an active tile assembly and give a detailed example of an aperiodic set of active tiles which hierarchically produces a self-similar L-shape tiling. This yields a technique utilizing active tiles for the assembly of aperiodic self-similar shapes