  We view random walks as the paths of foraging animals, perhaps searching for
food or avoiding predators while forming a mental map of their surroundings.
The formation of such maps requires them to memorise the locations they have
visited. We model memory using a kernel, proportional to the number of
locations recalled as a function of the time since they were first observed. We
give exact analytic expressions relating the elongation of the memorised walk
to the structure of the memory kernel, and confirm these by simulation. We find
that more slowly decaying memories lead to less elongated mental maps.
