(Color online) Distribution of human displacements (from record D1 and Figure 1(c) in Gonzalez et al. (12)). The length Δr is the travel distance. The distribution is fit with Eq. (2).
(Color online) Distribution of human displacements (from record D1 and Figure 1(C) in Gonzalez et al. (12)). The length Δr is the travel distance. The distribution is approximately reproduced within three consecutive ranges with incremental inverse power law functions proportional to 1/Δr β. We get: 1) β ≈ 1 for ; 2) β ≈ 2 for ; 3) β ≈ 3 for .
(Color online) Schematic representation of human motion with Lévy flights in three different displacement zone ranges. The bottom left corner represents the residence location where the walker returns. The regions with a higher density of displacements represent cities or towns (zone 1) where the walker stays longer. The distance among the cities classifies zone 2 or zone 3 according to whether the journey is medium or long. The shadowed areas represent the urban area where the benefits are assumed to be randomly/uniformly distributed. Displacements within these restricted areas yield to Pareto distribution with exponent β = 1 according to Eq. (5). Displacements between close areas of interest yield to Pareto distribution with exponent β = 2 according to Eq. (8).
(Color online) Reproduction of Figure 6 in Rhee et al. (18) which refers to a distribution of displacements at Disney World (Orlando, FL) by a sample of traces obtained from 18 volunteers that mainly walked in the park during holidays. The figure shows in the wide lighter (green) curve the authors’ original fit obtained with a truncated Pareto distribution that gives an exponent β = 1.86 for the entire range. The two narrow straight (red and blue) lines, instead, were added by me and highlight that the smallest displacement range up to 100–200 m is compatible with a Pareto distribution with β = 1, while the longer scale is compatible with a Pareto distribution with β = 2. Note that the statistics for displacements above approximately 1000 m is visibly poorer.
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