Definition of the Subject
Cities have been treated as systems for fifty years but only in the last two decades has the focus changed from aggregateequilibrium systems to more evolving systems whose structure emerges from the bottom up. We firstoutline the rudiments of the traditional approach focusing on equilibrium and then discuss how the paradigm has changed to one which treats cities asemergent phenomena generated through a combination of hierarchical levels of decision, driven in decentralized fashion. This is consistent with thecomplexity sciences which dominate the simulation of urban form and function. We begin however with a review of equilibrium models, particularlythose based on spatial interaction, and we then explore how simple dynamic frameworks can be fashioned to generate more realistic models. In exploringdynamics , nonlinear systems which admit chaos and bifurcation have relevance but recently more pragmaticschemes of structuring urban...
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- Agent‐based models:
Systems composed of individuals who act purposely in making locational/spatial decisions.
A process whereby divergent paths are generated in a trajectory of change in an urban system.
- City size distribution:
A set of cities ordered by size, usually population, often in rank order.
- Emergent patterns:
Land uses or economic activities which follow some spatial order.
- Entropy maximizing:
The process of generating a spatial model by maximizing a measure of system complexity subject to constraints.
A state of the urban system which is balanced and unchanging.
- Exponential growth:
The process whereby an activity changes through positive feedback on itself.
- Fast dynamics:
A process of frequent movement between locations, often daily.
The process whereby a system variable influences another variable, either positively or negatively.
- Fractal structure:
A pattern or arrangement of system elements that are self‐similar at different spatial scales.
- Land use transport model:
A model linking urban activities to transport interactions.
- Life cycle effects:
Changes in spatial location which are motivated by aging of urban activities and populations.
- Local neighborhood:
The space immediately around a zone or cell.
- Logistic growth:
Exponential growth capacitated so that some density limit is not exceeded.
- Lognormal distribution:
A distribution which has fat and long tails which is normal when examined on a logarithmic scale.
The process of generating synthetic populations from data which is collated from several sources.
- Model validation:
The process of calibrating and testing a model against data so that its goodness of fit is optimized.
Relationships which embody nth order effects of one variable on another.
- Network scaling:
The in‐degrees and out‐degrees of a graph whose nodal link volumes follow a power law.
- Population density profile:
A distribution of populations which typically follows an exponential profile when arrayed against distance from some nodal point.
- Power laws:
Scaling laws that order a set of objects according to their size raised to some power.
- Rank size rule:
A power law that rank orders a set of objects.
The process of generating changes as a consequence of a reaction to an existing state and interactions between states.
- Scale‐free networks:
Networks whose nodal volumes follow a power law.
- Segregation model:
A model which generates extreme global segregation from weak assumptions about local segregation.
The process of generating locational distributions according to a series of sub‐model equations or rules.
- Slow dynamics:
Changes in the urban system that take place over years or decades.
- Social physics:
The application of classical physical principles involving distance, force and mass to social situations, particularly to cities and their transport.
- Spatial interaction:
The movement of activities between different locations ranging from traffic distributions to migration patterns.
- Trip distribution:
The pattern of movement relating to trips made by the population, usually from home to work but also to other activities such as shopping.
- Urban hierarchy:
A set of entities physically or spatially scaled in terms of their size and areal extent.
- Urban morphology:
Patterns of urban structure based on the way activities are ordered with respect to their locations.
- Urban system:
A city represented as a set of interacting subsystems or their elements.
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Batty, M. (2009). Cities as Complex Systems: Scaling, Interaction, Networks, Dynamics and Urban Morphologies. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_69
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-75888-6
Online ISBN: 978-0-387-30440-3