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Fig. 6. The mean number, n_box, of boxes of size l_box required to cover the representations of the honeybee flights. Power-law scaling, n_boxl_box^-D is indicative of a scale-free characteristic with fractal dimension D. Power-law scaling with D=1.3 obtained from a linear least-squares fit (r²=0.99) is indicated. The insert shows the n_box of boxes of size l_box required to cover simulated Lévy-flights with µ=2. The number of straight-line flights within the simulated Lévy-flights is equal to the mean number of straight-line flights in the representations of the honeybee flights. The model predicts that D=1.2. A similar level of correspondence between the fractal dimension of the representations of bee flights and simulated Lévy flights with µ=2 is also attained when fractal dimensions are calculated using the method of dividers rather than the box-counting method.

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