Figure 1.

Relation between angular speed and path curvature in fly larvae tracing different trajectories. (a) Trajectory of the centroid position of one representative larva in the overshoot condition (blue circle indicates starting position). (b) Scatterplot of instantaneous angular speed A and local path curvature C on log₁₀–log₁₀ scale. All data points (red dots, n = 2100) sampled at equal time intervals along the same trajectory as in (a) were included. The data were fitted by the power function A(t) = kC(t)^β (black line) with β-exponent and variance accounted for (r²) as indicated (top right). (c) Temporal evolution of the path curvature (green) and angular speed (magenta) for the same data as in (a–b). (d) Centroid trajectory of a larva in the approach condition. Key movement variables are identified at an arbitrary point along the trajectory: C is the curvature of the osculating circle of radius R, α is the phase angle of the tangent and the angular speed A is the time derivative of α. (e) Log–log plot of angular speed versus curvature for the same trajectory as in (d). (f) Summary boxplot statistics for β-exponent of individual animals in the three different groups: overshoot (n = 42), approach (n = 40) and dispersal (n = 41). Outliers are orange dots. (g) Centroid trajectory of a larva in the dispersal condition. (h) Log–log plot of angular speed versus curvature for the same trajectory as in g. (i) Summary boxplot statistics for r² in the three groups. (Online version in colour.)