Dimensionality and Dynamics in the Behavior of C. elegans
(A) Raw image in the tracking microscope. (B) The curve through the center of the body. The black circle marks the head. (C) Distances along the curve (arclength s) are measured in normalized units, and we define the tangent (s) and normal (s) to the curve at each point. The tangent points in a direction θ(s), and variations in this angle correspond to the curvature κ(s) = dθ(s)/ds. (D) All images are rotated so that 〈θ〉 = 0; therefore θ (s) provides a description of the worm's shape that is independent of our coordinate system, and intrinsic to the worm itself.