  We extend a recently proposed model (Chaudhuri et al., EPL 87, 20003 (2009))
aiming to describe the formation of fascicles of axons during neural
development. The growing axons are represented as paths of interacting directed
random walkers in two spatial dimensions. To mimic turnover of axons, whole
paths are removed and new walkers are injected with specified rates. In the
simplest version of the model, we use strongly adhesive short-range inter-axon
interactions that are identical for all pairs of axons. We generalize the model
to adhesive interactions of finite strengths and to multiple types of axons
with type-specific interactions. The dynamic steady state is characterized by
the position-dependent distribution of fascicle sizes. With distance in the
direction of axon growth, the mean fascicle size and emergent time scales grow
monotonically, while the degree of sorting of fascicles by axon type has a
maximum at a finite distance. To understand the emergence of slow time scales,
we develop an analytical framework to analyze the interaction between
neighboring fascicles.
