Fig. 4. Geometric analysis of the interaction between unc-23 pirouette behavior and turning bias. An idealized unc-23 mutant animal moves with a constant clockwise turning bias and produces pirouettes with either a 180° or 0° change in bearing. The animal moves in a radial gradient from the starting position indicated by asterisks; the gradient peak is at the plus sign. Shown are four cases in which the animal initiates pirouettes in only one quadrant (I, II, III or IV) that is defined relative to direction of the gradient peak (see diagrams adjacent to each track). (A) Quadrant IV pirouettes produce a clockwise spiral track. This type of track corresponds to the unc-23 tracks reported in the original study (Ward, 1973). (B) Quadrant I pirouettes produce a counterclockwise spiral track centered on the radial gradient peak. This type of track corresponds to the real unc-23 track shown in Fig. 1Bii. (C,D) Quadrants II or III pirouettes produce spiral tracks leading down the gradient away from the gradient peak.