Tip-driven growth processes underlie the development of many plants. To date,
tip-driven growth processes have been modelled as an elongating path or series
of segments without taking into account lateral expansion during elongation.
Instead, models of growth often introduce an explicit thickness by expanding
the area around the completed elongated path. Modelling expansion in this way
can lead to contradictions in the physical plausibility of the resulting
surface and to uncertainty about how the object reached certain regions of
space. Here, we introduce "fiber walks" as a self-avoiding random walk model
for tip-driven growth processes that includes lateral expansion. In 2D, the
fiber walk takes place on a square lattice and the space occupied by the fiber
is modelled as a lateral contraction of the lattice. This contraction
influences the possible follow-up steps of the fiber walk. The boundary of the
area consumed by the contraction is derived as the dual of the lattice faces
adjacent to the fiber. We show that fiber walks generate fibers that have
well-defined curvatures, enable the identification of the process underlying
the occupancy of physical space. Hence, fiber walks provide a base from which
to model both the extension and expansion of physical biological objects with
finite thickness.Comment: Plos One (in press
