the book referred to by chris can be downloaded free at

http://www.fractalcities.org

Mike

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Michael Batty
Centre for Advanced Spatial Analysis (CASA)
University College London (UCL)
90 Tottenham Court Road, London W1T 4TJ, UK

Tel  44 (0) 20 3108 3877 Mobile 44 (0) 7768 423 656
http://www.complexcity.info

t @jmichaelbatty

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From: Complexity & Planning [[log in to unmask]] on behalf of Chris Webster [[log in to unmask]]
Sent: 15 July 2012 16:06
To: [log in to unmask]
Subject: fractals, space-filling and infrastructure-development sequencing

I have always suspected that cities that have a strong evolutionary history of incremental growth with a lot of retrofitting of infrastructure (as opposed to comprehensively planned cities (or for cities also read neighbourhoods at a different scale), have more efficient space filling. I imagine that a read of Batty and Longley's (1993?) book on fractals would support this - it's a long time since I read it. Retro-fitted transport infrastructure to increase capacity has the effect of increasing opportunities for gains from trade in land and gives rise to property rights fragmentation and economic deepening. The fractal dimension/ degree of space filling of a city is one performance measure of efficiency that could be correlated with the history of infrastructure-population growth sequencing (I'll send some references to research on this later - sent to me by Alain Chiaradia). The equivalent economic indicator at one level is, simply, land value. Land value is an indicator of realised gains from trade in the land market. Newly created accessibility through a new transit line for example, increase the number of possible exchange partners in urban economy and increase derived-demand in the land market. The result is densification, which is the physical manifestation of property rights deepening and fragmentation. The deepening of property rights in land is itself a fractal process as every subdivision of ownership creates new cadastral boundaries which can be subject to further trading of rights (see Webster and Lai 2003 Chapter 5 - new updated edition coming out next year hopefully by the way). So at one level, land values can be taken as a measure of the spatial efficiency of a city - and infrastructure-population or service-population sequencing could be correlated with land value movements and outcomes.
At another level, however, it may not be as simple as high land-values=most efficient land use. London with more key-worker housing may have higher aggregate urban GDP and higher aggregate land value than with less key-worker housing, for example. So some loss of local land value (by regulation or legal devices) may increase global urban land value. It is the economic content of space-filling, not space-filling per se that is of most interest when we are examining the efficiency of urban form. This might mean that infrastructure-population sequencing is best correlated with measures of total city productivity and/or land value - over time or between cities.
Chris