Fig. 5. Power-law scaling of the root-mean-square, F, net displacement indicative of the presence of long-range correlations, demonstrating that the honeybee flights are scale-free. The averaging is over the `searching phases' of 39 bees. Approximate power-law scaling behaviour with =0.85 extending over about one decade is indicated (straight line). This scaling and others presented later are not sensitively dependent upon the presence or absence of four non-returning bee tracks within the averaging. The scaling exponent, , does not change significantly when the angle (90°) between successive flight segments used to define a change in flight orientation is changed by ±30°.