  Organisms move through the world by changing their shape, and here we explore
the mapping from shape space to movements in the nematode C. elegans as it
crawls on a planar agar surface. We characterize the statistics of the
trajectories through the correlation functions of the orientation angular
velocity, orientation angle and the mean-squared displacement, and we find that
the loss of orientational memory has significant contributions from both
abrupt, large amplitude turning events and the continuous dynamics between
these events. Further, we demonstrate long-time persistence of orientational
memory in the intervals between abrupt turns. Building on recent work
demonstrating that C. elegans movements are restricted to a low-dimensional
shape space, we construct a map from the dynamics in this shape space to the
trajectory of the worm along the agar. We use this connection to illustrate
that changes in the continuous dynamics reveal subtle differences in movement
strategy that occur among mutants defective in two classes of dopamine
receptors.
