Fractal patterns represent an important classof aperiodic arrangements. Generating fractalstructures by self-assembly is a majorchallenge for nanotechnology. The specificityof DNA sticky-ended interactions and thewell-behaved structural nature of DNAparallelogram motifs has previously led to aprotocol that appears likely to be capable ofproducing fractal constructions [A. Carbone andN.C. Seeman, A route to fractal DNAassembly, Natural Computing1,469–480, 2002]. That protocol dependson gluing the set of tiles with special `gluetiles' to produce the fractal structure. It ispossible to develop a fractal-assembly protocolthat does not require the participation ofgluing components. When designed with similarDNA parallelogram motifs, the protocol involvessixteen specific tiles, sixteen closely relatedtiles, and a series of protecting groups thatare designed to be removed by the introductionof specific strands into the solution. Onenovel aspect of the construction on thetheoretical level is the interplay of bothgeometry and coding in tile design. A secondfeature, related to the implementation, is thenotion of generalized protecting groups.
coding of tiles DNA assembly DNA molecules DNA nanotechnology geometry of tiles Sierpinski fractals tiling