Fig. 5. Spatiotemporal thermal gradients. Representative trajectories of worms navigating spatiotemporal thermal gradients with fixed steepness in the radial direction and with superposed, spatially uniform, sine-wave temporal variation. Each trajectory shows a single period of persistent forward movement exhibited by a worm navigating these gradients, with positions along each run indicated at 10 s intervals. (A) When worms navigate a spatiotemporal thermal gradient with 0.4°C cm^-1 spatial steepness and sine-wave temporal variation with 0.05°C amplitude and 60 s period, prolonged floral trajectories emerge as the worm follows each isotherm during cycles of contraction and expansion. (B) Floral trajectories of worms navigating a spatiotemporal thermal gradient with 0.4°C cm^-1 spatial steepness and sine-wave temporal variation with 0.1°C amplitude and 120 s period. (C) Floral trajectories are largely replaced by looping trajectories when worms navigate a spatiotemporal thermal gradient with 0.4°C cm^-1 spatial steepness and sine-wave temporal variation with 0.2°C amplitude and 120 s period. (D) Floral trajectories of worms navigating a spatiotemporal thermal gradient with the same temporal variation as in Fig. 4C, but with a 0.7°C spatial steepness. (E) The relative appearance of floral and looping trajectories on spatiotemporal gradients with fixed 0.4°C cm^-1 spatial steepness depends on the steepness of the superposed temporal gradient. The steepness of the temporal gradient is proportional to its amplitude (T₀) and frequency (). The floral trajectories dominate when T₀ is small (above the dotted line), and are replaced by looping trajectories when T₀ is large (below the dotted line). The shading of each circle corresponds to the fraction of floral trajectories in a dataset corresponding to 300 tracks. The dotted line indicates the approximate boundary between loop-like and flower-like trajectories, occurring as approaches 1; the dotted line shows 0.4.