HD ring attractor properties. A, From left to right, Panels 1–3 represent LMNcw tuning curves sampled exclusively during CW (orange), CCW (green), and no-turn/straight states (STR) (blue). Panel 4 represents the average over all conditions. Panel 5 compares the average tuning curves in the previous panels (thick black lines). CW and CWW tuning curves are offset in CCW and CW directions, respectively, reflecting anticipatory firing. B, Same data for LMNccw. Panels 1–4 all represent data from the entire HD ensemble shifted to have tuning centered at 0 (for details, see Materials and Methods). The angular scale increases CCW following the standard mathematic convention. C, Weak, prolonged stimulation (here 300 ms duration, applied at 1200 ms) gradually shifts the activity packet. D, Strong, brief stimulation (here 100 ms duration, applied at 1050 ms) leads to a jump of the activity packet to a new HD. The y-axis denotes the neuron number. Each LMN ring is comprised of 720 neurons, with tuning covering 0°-360°. E, Three representative samples (of 30) of drift over 5 min of active exploration without visual feedback, showing the absolute value of the HD error. Average drift is 0.38°/s based on the HD error after 3 min.