Fig. 6. The mean number, nbox, of boxes of size
lbox required to cover the representations of the honeybee
flights. Power-law scaling,
nbox
lbox-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
nbox of boxes of size lbox 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.