Effect of systematic initial phase shifts on grid cell firing patterns using different values of a and b in the formula for translation of grid fields in horizontal (b) and vertical (a) directions. The two columns show the effect of simultaneously setting b at 0 or 180 degrees (0 or π radians). The four rows show the effect of phase shifts using a=0, 90, 180 and 240 degrees (0, π/2, π, 3π/2 radians).