We exploit the reduced space of C. elegans postures to develop a novel tracking algorithm which captures both simple shapes and also self-occluding coils, an important, yet unexplored, component of 2D worm behavior. We apply our algorithm to show that visually complex, coiled sequences are a superposition of two simpler patterns: the body wave dynamics and a head-curvature pulse. We demonstrate the precise Ω-turn dynamics of an escape response and uncover a surprising new dichotomy in spontaneous, large-amplitude coils; deep reorientations occur not only through classical Ω-shaped postures but also through larger postural excitations which we label here as δ-turns. We find that omega and delta turns occur independently, suggesting a distinct triggering mechanism, and are the serpentine analog of a random left-right step. Finally, we show that omega and delta turns occur with approximately equal rates and adapt to food-free conditions on a similar timescale, a simple strategy to avoid navigational bias.