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Self-Organisation in Spatial Systems-From Fractal Chaos to Regular Patterns and Vice Versa.

Banaszak M, Dziecielski M, Nijkamp P, Ratajczak W - PLoS ONE (2015)

Bottom Line: This study offers a new perspective on the evolutionary patterns of cities or urban agglomerations.Such developments can range from chaotic to fully ordered.Our approach is dynamic in nature and forms a generalisation of hierarchical principles in geographic space.

View Article: PubMed Central - PubMed

Affiliation: Faculty of Physics, A. Mickiewicz University, ul. Umultowska 85, 61-614 Poznan, Poland.

ABSTRACT
This study offers a new perspective on the evolutionary patterns of cities or urban agglomerations. Such developments can range from chaotic to fully ordered. We demonstrate that in a dynamic space of interactive human behaviour cities produce a wealth of gravitational attractors whose size and shape depend on the resistance of space emerging inter alia from transport friction costs. This finding offers original insights into the complex evolution of spatial systems and appears to be consistent with the principles of central place theory known from the spatial sciences and geography. Our approach is dynamic in nature and forms a generalisation of hierarchical principles in geographic space.

No MeSH data available.


Related in: MedlinePlus

a) Chaos and order in a hexagon with cities of equal masses, with the following parameters: μ = 0.09, m = 1, k = 1, and h = 0.02, which will be described below. Cities, indicated by black circles, have the following coordinates: , (0.0,2.0), , , (0.0, −2.0),and . The distance between neighbouring cities is 2; b) three trajectories; c) transition to order in hexagonally-placed cities with μ = 0.7.
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pone.0136248.g001: a) Chaos and order in a hexagon with cities of equal masses, with the following parameters: μ = 0.09, m = 1, k = 1, and h = 0.02, which will be described below. Cities, indicated by black circles, have the following coordinates: , (0.0,2.0), , , (0.0, −2.0),and . The distance between neighbouring cities is 2; b) three trajectories; c) transition to order in hexagonally-placed cities with μ = 0.7.

Mentions: Our study will present the equations of motion (see Eq 10) for simulating an ideal-typical hierarchical spatial system of places or settlements. The simulation experiment presented below is based on the theory of geographical potential, which is an important component of social physics that has been applied in socio-economic geography for more than 100 years (starting with [10], [11, 12] and [13], and more recently [14, 15]). The premise of our study is that humans are ‘thinking particles’ in geographical space, who interact on the basis of economic, social or cognitive proximity. The behavioural foundation and justification of the concept of ‘social physics’ can be found inter alia in [16], where the authors provide a clear methodological underpinning for a behavioural conceptualisation micro processes in relation to macro outcomes. Clearly, human systems are not identical to statistical mechanics systems, but their dynamic behaviour in geographic space may exhibit similar movements. In accordance with the idea of geographical potential, our experiment rests on the assumption that settlement units, e.g. towns and cities, produce attraction areas, or gravitational attractors for agents. This means that an arbitrary, uninformed agent who enters the attraction space spanned by various towns tends to take first a chaotic path, before finally being attracted by one of the towns. It will ultimately find itself in its gravitational attractor. This situation is illustrated in Fig 1a which depicts six towns in a hexagonal CPT pattern. For numerical calculations, we use a 2-dimensional grid. The x and y coordinates are set from -5 to 5, so that we have a 10 by 10 field. The starting points of agents are located at equal increments of 1/700. So we have 7,000 points on the x axis and 7,000 points on the y axis, which gives a total of 49 million starting points. If the agent starts from point (-5,5) and stops on a hexagon point, for example (0,2) labelled green, then this starting point will also be labelled green. This procedure is repeated for every starting point with a corresponding colour.


Self-Organisation in Spatial Systems-From Fractal Chaos to Regular Patterns and Vice Versa.

Banaszak M, Dziecielski M, Nijkamp P, Ratajczak W - PLoS ONE (2015)

a) Chaos and order in a hexagon with cities of equal masses, with the following parameters: μ = 0.09, m = 1, k = 1, and h = 0.02, which will be described below. Cities, indicated by black circles, have the following coordinates: , (0.0,2.0), , , (0.0, −2.0),and . The distance between neighbouring cities is 2; b) three trajectories; c) transition to order in hexagonally-placed cities with μ = 0.7.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4581867&req=5

pone.0136248.g001: a) Chaos and order in a hexagon with cities of equal masses, with the following parameters: μ = 0.09, m = 1, k = 1, and h = 0.02, which will be described below. Cities, indicated by black circles, have the following coordinates: , (0.0,2.0), , , (0.0, −2.0),and . The distance between neighbouring cities is 2; b) three trajectories; c) transition to order in hexagonally-placed cities with μ = 0.7.
Mentions: Our study will present the equations of motion (see Eq 10) for simulating an ideal-typical hierarchical spatial system of places or settlements. The simulation experiment presented below is based on the theory of geographical potential, which is an important component of social physics that has been applied in socio-economic geography for more than 100 years (starting with [10], [11, 12] and [13], and more recently [14, 15]). The premise of our study is that humans are ‘thinking particles’ in geographical space, who interact on the basis of economic, social or cognitive proximity. The behavioural foundation and justification of the concept of ‘social physics’ can be found inter alia in [16], where the authors provide a clear methodological underpinning for a behavioural conceptualisation micro processes in relation to macro outcomes. Clearly, human systems are not identical to statistical mechanics systems, but their dynamic behaviour in geographic space may exhibit similar movements. In accordance with the idea of geographical potential, our experiment rests on the assumption that settlement units, e.g. towns and cities, produce attraction areas, or gravitational attractors for agents. This means that an arbitrary, uninformed agent who enters the attraction space spanned by various towns tends to take first a chaotic path, before finally being attracted by one of the towns. It will ultimately find itself in its gravitational attractor. This situation is illustrated in Fig 1a which depicts six towns in a hexagonal CPT pattern. For numerical calculations, we use a 2-dimensional grid. The x and y coordinates are set from -5 to 5, so that we have a 10 by 10 field. The starting points of agents are located at equal increments of 1/700. So we have 7,000 points on the x axis and 7,000 points on the y axis, which gives a total of 49 million starting points. If the agent starts from point (-5,5) and stops on a hexagon point, for example (0,2) labelled green, then this starting point will also be labelled green. This procedure is repeated for every starting point with a corresponding colour.

Bottom Line: This study offers a new perspective on the evolutionary patterns of cities or urban agglomerations.Such developments can range from chaotic to fully ordered.Our approach is dynamic in nature and forms a generalisation of hierarchical principles in geographic space.

View Article: PubMed Central - PubMed

Affiliation: Faculty of Physics, A. Mickiewicz University, ul. Umultowska 85, 61-614 Poznan, Poland.

ABSTRACT
This study offers a new perspective on the evolutionary patterns of cities or urban agglomerations. Such developments can range from chaotic to fully ordered. We demonstrate that in a dynamic space of interactive human behaviour cities produce a wealth of gravitational attractors whose size and shape depend on the resistance of space emerging inter alia from transport friction costs. This finding offers original insights into the complex evolution of spatial systems and appears to be consistent with the principles of central place theory known from the spatial sciences and geography. Our approach is dynamic in nature and forms a generalisation of hierarchical principles in geographic space.

No MeSH data available.


Related in: MedlinePlus