Zipf’s law is a very tight constraint on the class of admissible models of local growth. It says that for most countries the size distribution of cities strikingly fits a power law: the number of cities with populations greater than S is proportional to 1/S. Suppose that, at least in the upper tail, all cities follow some proportional growth process (this appears to be verified empirically). This automatically leads their distribution to converge to Zipf’s law. I.

Cities have been treated as systems for fifty year but only in the last two decades has the focus changed from aggregate equilibrium systems to more evolving systems whose structure merges from the bottom up. We first outline the rudiments of the traditional approach focusing on equilibrium and then discuss how the paradigm has changed to one which treats cities as emergent phenomena generated through a combination of hierarchical levels of decision, driven in decentralized fashion. This is consistent with the complexity sciences which dominate the simulation of urban form and function. We begin however with a review of equilibrium models, particularly those based on spatial interaction, and we then explore how simple dynamic frameworks can be fashioned to generate more realistic models. In exploring dynamics, nonlinear systems which admit chaos and bifurcation have relevance but recently more pragmatic schemes of structuring urban models based on cellular automata and agent-based modeling principles have come to the fore. Most urban models deal with the city in terms of the location of its economic and demographic activities but there is also a move to link such models to urban morphologies which are clearly fractal in structure. Throughout this chapter, we show how key concepts in complexity such as scaling, self-similarity and far-from-equilibrium structures dominate our current treatment of cities, how we might simulate their functioning and how we might predict their futures. We conclude with the key problems that dominate the field and suggest how these might be tackled in future research.

This paper reviews the progress that has been made over the last half-century in modeling and analyzing the growth of transportation networks. An overview of studies has been provided following five main streams: network growth in transport geography; traffic flow, transportation planning, and network growth; statistical analyses of network growth; economics of network growth; and network science. In recognition of the vast advances through decades in terms of exploring underlying growth mechanisms and developing effective network growth models, the authors also point out the challenges that are faced to model the complex process of transport development.

This paper reviews the progress that has been made over the last half-century in modeling and analyzing the growth of transportation networks. An overview of studies has been provided following five main streams: network growth in transport geography; traffic flow, transportation planning, and network growth; statistical analyses of network growth; economics of network growth; and network science. In recognition of the vast advances through decades in terms of exploring underlying growth mechanisms and developing effective network growth models, the authors also point out the challenges that are faced to model the complex process of transport development. 1