The spatially explicit perspective of space use I (N)under variable ρ (same data as in Figure2) and constant grid resolution. Both LW and BM confirms regression slope z ≈ 1 in double-log plot of I(N). Increased influence from return steps leads to z ≈ 0.5 for ρ 1 (colour references for respective ρ as in Figure 3), which is expected from β = 2 and infinite memory. The transition zone from auto-correlated towards non-auto-correlated spatial relocations (ρ ≈ 1; blue circles) leads to an intermediate power exponent. When analyzing real data in a similar manner, grid resolution should be varied to fit the scale where intercept c ≈ 1 [log(c) = 0)]. This unit pixel size then equals the movement’s characteristic spatial scale.