  We study a simple model in which the growth of a network is determined by the
location of one or more random walkers. Depending on walker speed, the model
generates a spectrum of structures situated between well-known limiting cases.
We demonstrate that the average degree observed by a walker is related to the
global variance. Modulating the extent to which the location of node attachment
is determined by the walker as opposed to random selection is akin to scaling
the speed of the walker and generates new limiting behavior. The model raises
questions about energetic and computational resource requirements in a physical
instantiation.
