Abstract
RNA cotranscriptional folding has been just experimentally proven capable of self-assembling a rectangular tile at nanoscale in vivo (RNA origami). We initiate the theoretical study on the algorithmic self-assembly of shapes by cotranscriptional folding using a novel computational model called the oritatami system. We propose an oritatami system that folds into an arbitrary finite portion of the Heighway dragon fractal, also-known as the paperfolding sequence \(P = \mathrm{RRLRRLLR} \cdots \). The i-th element of P can be obtained by feeding i in binary to a 4-state DFA with output (DFAO). We implement this DFAO and a bit-sequence bifurcator as modules of oritatami system. Combining them with a known binary counter yields the proposed system.
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