Figure 3. Example of motor (i.e. current corrected) path of a MH turtle (MH5), which was able to come close to home (13 km) in four days but missed it and was eventually unable to reach it.

In the special frame of reference used here, the X axis corresponds to the home direction, and the Y axis to the orthogonal direction (X_k = X_k−1+l.cos(θ_k−γ_{k −1}); Y_k = Y_k−1+l.sin(θ_k−γ_{k −1}), where l = 5 km is the step length, θ_k is the orientation of the k ^th step, and γ_{k −1} is the goal direction at the k−1^th location). The inset shows the ground-related path in the geographic frame of reference. It can be clearly seen that this magnetically treated turtle was quite efficient in moving in the home direction during the first part of its homing path: to come within 13 km of home, she swan only 305 km (61 5-km steps) for a move of 239 km in the goal direction (navigational efficiency: 0.78).