The pleasure of walking in a neighbourhood: the pedestrian route network and its fractal dimension as a tool for the assessment of the right balance between chaos and order

Many cities suffer from a lack of walkability. Besides physical preconditions like safe sidewalks and pedestrianized areas the density of the pedestrian network and the planar distribution of routes opening up the area of a quarter or the city. The fractal dimension (FD) is a measure that describes how far a pattern or grid spans and covers a two dimensional area. For areas in the field of view (like paintings) literature reports that values between 1.3 and 1.9 are perceived as most agreeable and stress reducing. This paper investigates if the FD can also be applied to assess the walkability of pedestrian networks. That is not trivial because, for a walking person, the network is not in direct field of view but only perceived with all senses. The research question is, if pedestrian networks behave fractal in the range where they are delivering best preconditions for walkability. For real networks, the loop-wise calculation of FD is best appropriate; here a box-counting method is used. The box edge length corresponds to the distance that a pedestrian must walk ahead until the next possibility where a decision to turn or not appears. So more such junctions exist, so more walkable is the quarter. Typical preferred distances are few meters to about 50 m. The results show well, that for as walkable perceived quarters, the network behaves in fact fractal with FD in the preferred range 1.3–1.9 and at box edge length’ of 5–50 m – and vice versa. Objects of investigation were pedestrian networks out of the city of Hamburg, Germany, one car-oriented, one that is perceived as walkable and one of the newly constructed quarter HafenCity. The car-oriented quarter is widely out of the described range, the walkable one widely in. Finally, historical cities (Salamanca, Spain and the Islamic town Harar Jugol, Ethiopia) were analysed to find out if their networks (out of times without cars) are walkable and behave fractal. As to be expected, both could be confirmed. It can be concluded, that FD can well be used as an indicator for the walkability of pedestrian route networks.