Speaker: Dr Florent Becker, University of Orléans

Since time immemorial, women and men have yearned for nano-trinkets made of DNA. Since the nineties, following seminal works by Reif, Adleman, Winfree, then Rothemund, Woods and many others, this peculiar desire has come closer and closer to being fulfilled: it is possible to cleverly devise DNA sequences with interactions mimicking those of abstract tiles trapped in an ideal discrete plane. Said tiles bear a colour on each side, which stand for the DNA sequences. Like coral on a reef, they accrete around a seed: each time a tile comes close to an empty position where the colors match its own, it settles there and extends the pattern.

The bee’s knees of shapes to self-assemble has been discrete self-similar fractals. Because of their delicate, lace-like structure, it has been conjectured that they were not dense enough to harbour a computation describing their own shape. Hence, went the reasoning, they cannot be self-assembled, but only obtained by extrinsic means. Yet, as this talk will detail, use of clever tools from the theory of computation give a way around this obstacle, allowing most fractals to be self-assembled. I will present the principles of two such constructions. The first one leverages Quines, that is programs which output their own source-code, and yields the self-assembly of one fractal shape. The second one uses “self-describing circuits” and generalizes to a whole class of fractal shapes.

Despite these results, the reasoning behind the disproved conjecture has a nugget of truth: some fractal shapes are indeed too frail for self-assembly. I will detail which and the high-level reason why.

This talk does not require an advanced mathematical or computer science background, as I will strive to start from scratch.

This is an virtual event held in Hamilton Institute Seminar room (317), 3rd floor Eolas Building, North Campus with virtual participation details here: Zoom .