  An oritatami system (OS) is a theoretical model of self-assembly via
co-transcriptional folding. It consists of a growing chain of beads which can
form bonds with each other as they are transcribed. During the transcription
process, the $\delta$ most recently produced beads dynamically fold so as to
maximize the number of bonds formed, self-assemblying into a shape
incrementally. The parameter $\delta$ is called the delay and is related to the
transcription rate in nature.
  This article initiates the study of shape self-assembly using oritatami. A
shape is a connected set of points in the triangular lattice. We first show
that oritatami systems differ fundamentally from tile-assembly systems by
exhibiting a family of infinite shapes that can be tile-assembled but cannot be
folded by any OS. As it is NP-hard in general to determine whether there is an
OS that folds into (self-assembles) a given finite shape, we explore the
folding of upscaled versions of finite shapes. We show that any shape can be
folded from a constant size seed, at any scale n >= 3, by an OS with delay 1.
We also show that any shape can be folded at the smaller scale 2 by an OS with
unbounded delay. This leads us to investigate the influence of delay and to
prove that, for all {\delta} > 2, there are shapes that can be folded (at scale
1) with delay {\delta} but not with delay {\delta}'<{\delta}. These results
serve as a foundation for the study of shape-building in this new model of
self-assembly, and have the potential to provide better understanding of
cotranscriptional folding in biology, as well as improved abilities of
experimentalists to design artificial systems that self-assemble via this
complex dynamical process.
