RNA cotranscriptional folding is the phenomenon in which an RNA transcript folds upon itself while being synthesized out of a gene. The oritatami system is a computation model of this phenomenon, which lets its sequence (transcript) of beads (abstract molecules) fold cotranscriptionally by the interactions between beads according to the binding ruleset. In such models based on self-assembly, one of the key questions is the ability to construct fractal structures. We focus on the problem of generating an infinite fractal curves using a cyclic oritatami system, which has an infinite periodic transcript. We first establish a formal definition of drawing a curve using an oritatami system, proposing conditions and restrictions with reference to prior oritatami designs for possibly infinite conformations. Under such definition, we prove that it is impossible to draw a Koch curve or a Minkowski curve infinitely. We then establish sufficient conditions of infinite aperiodic curves that a cyclic oritatami system cannot fold.

RNA 共转录折叠是一种 RNA 转录物在从基因合成时自身折叠的现象。oritatami 系统是这种现象的计算模型，它让珠子（抽象分子）的序列（转录本）根据绑定规则集通过珠子之间的相互作用共转录折叠。在这种基于自组装的模型中，关键问题之一是构建分形结构的能力。我们专注于使用具有无限周期转录本的循环 oritatami 系统生成无限分形曲线的问题。我们首先建立了使用 oritatami 系统绘制曲线的正式定义，并参考先前的 oritatami 设计提出了可能无限构象的条件和限制。在这样的定义下，我们证明了不可能无限地绘制 Koch 曲线或 Minkowski 曲线。然后，我们建立了循环 oritatami 系统不能折叠的无限非周期曲线的充分条件。