Two main theses and a more general one underlie this paper. The first thesis is that the distribution of some of the configurational indices narrowly approximates a Paretian trend, thus appearing as a power function of their rank: the distinguishing feature, in fact, is not only the presence of a few number of lines with huge choice values, but also that those few lines actually coexist with a large number of scarcely chosen ones; number that increases as values decrease, what appears simply defying a bell curve. The absence of a peak in a power law distribution implies that there is no such a thing as a scale: we observe a continuous hierarchy of lines, spanning from those with highest values, followed by some less frequently present in the connection paths, then by dozen that are even more neglected, up to the more and more numerous deserted ones, so as to conform the urban grid to a fractal structure, according to that power law distribution that was acknowledged as a ‘patent signature’ of self-organization in complex systems (Jiang, 2007; Barabasi, 2014). Yet, if this law actually appears working well for the smallest ranks, it doesn’t fit the same for biggest ranks: a better fitting can be obtained multiplying the power law by an exponential function, thus providing the Zipf law with a smooth exponential cut-off. The second thesis is that such distribution decays in sprawled settlements, whose growth is actually characterized by low density, scattered urbanization and leapfrogging: here the results of some case studies indicate the presence of an abrupt cut-off in the distribution of choice, sharply breaking its tail; the more dispersed is actually the external development, the sooner and more steeply the tail appears to decay. In such cases a double slope seems to arise, so that the distribution of choice almost appears as a two regimes power law, composed by the initial Zipf law and followed by a steep sloping decay. A more general thesis gathers the two above: it will be argued that sprawl is mainly a relational phenomenon. Commonly perceived in the forms of traffic congestion, lack of pedestrian movement, depletion of inner cores, external concentration of shopping centres, absence of functional variety, landscape desolation, loss of local identities: all issues whose primary cause can be found in the configurational state, according to a clear logic and in measurable terms. Whose distinctive hallmark seems to be, among others, just the sharp cut-off of the tail in the distribution of choice, which materializes the breaking in the scale invariance of the system. The findings of several case studies seem to validate the thesis above: most of the phenomena that for decades now have been feeding the debate on urban sprawl appear anything but the predictable effects of the changes of spatial relationships caused by the suburbanization; whose clue can be detected in the slope of this function, the threshold from which it starts, the sharpness of the fracture with the initial curve. What will also provide some guidelines for rectifying the fracture and recomposing the tail.
When cities lose their tail: sprawl as a configurational matter
Cutini V.
2019-01-01
Abstract
Two main theses and a more general one underlie this paper. The first thesis is that the distribution of some of the configurational indices narrowly approximates a Paretian trend, thus appearing as a power function of their rank: the distinguishing feature, in fact, is not only the presence of a few number of lines with huge choice values, but also that those few lines actually coexist with a large number of scarcely chosen ones; number that increases as values decrease, what appears simply defying a bell curve. The absence of a peak in a power law distribution implies that there is no such a thing as a scale: we observe a continuous hierarchy of lines, spanning from those with highest values, followed by some less frequently present in the connection paths, then by dozen that are even more neglected, up to the more and more numerous deserted ones, so as to conform the urban grid to a fractal structure, according to that power law distribution that was acknowledged as a ‘patent signature’ of self-organization in complex systems (Jiang, 2007; Barabasi, 2014). Yet, if this law actually appears working well for the smallest ranks, it doesn’t fit the same for biggest ranks: a better fitting can be obtained multiplying the power law by an exponential function, thus providing the Zipf law with a smooth exponential cut-off. The second thesis is that such distribution decays in sprawled settlements, whose growth is actually characterized by low density, scattered urbanization and leapfrogging: here the results of some case studies indicate the presence of an abrupt cut-off in the distribution of choice, sharply breaking its tail; the more dispersed is actually the external development, the sooner and more steeply the tail appears to decay. In such cases a double slope seems to arise, so that the distribution of choice almost appears as a two regimes power law, composed by the initial Zipf law and followed by a steep sloping decay. A more general thesis gathers the two above: it will be argued that sprawl is mainly a relational phenomenon. Commonly perceived in the forms of traffic congestion, lack of pedestrian movement, depletion of inner cores, external concentration of shopping centres, absence of functional variety, landscape desolation, loss of local identities: all issues whose primary cause can be found in the configurational state, according to a clear logic and in measurable terms. Whose distinctive hallmark seems to be, among others, just the sharp cut-off of the tail in the distribution of choice, which materializes the breaking in the scale invariance of the system. The findings of several case studies seem to validate the thesis above: most of the phenomena that for decades now have been feeding the debate on urban sprawl appear anything but the predictable effects of the changes of spatial relationships caused by the suburbanization; whose clue can be detected in the slope of this function, the threshold from which it starts, the sharpness of the fracture with the initial curve. What will also provide some guidelines for rectifying the fracture and recomposing the tail.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
