Self-organized criticality and urban development

Urban society is undergoing as profound a spatial transformation as that as sociated with the emergence of the industrial city two centuries ago. To de scribe and measure this transition, we introduce a nea theory based on the concept that large-scale, complex systems composed of many interacting elem ents, show a surprising degree of resilience to change, holding themselves at critical levels for long periods until conditions emerge which move the system, often abruptly, to a new threshold. This theory is called 'self-org anized criticality' it is consistent with systems in which global patterns emerge from local action which is the hallmark of self-organization, and it is consistent with developments in system dynamics and their morphology wh ich find expression in fractal geometry and weak chaos theory, We illustrat e the theory using a unique space-time series of urban development for Buff alo, Western New York, which contains the locations of ol er one quarter of a million sites coded by their year of construction and dating back to 177 3, some 60 years before the city began to develop. Vile measure the emergen ce and growth of the city using urban density functions from which measures of fractal dimension are used to construct grow th paths of;he way the cit y has grown to fill its region, These phase portraits suggest the existence of transitions between the frontier, the settled agricultural region, the centralized industrial city and the decentralized postindustrial city;, and our analysis reveals that Buffalo has maintained itself at a critical thre shold since the emergence of the automobile city some 70 years ago, Our imp lied speculation is: how long will this kind of urban form be maintained in the face of seemingly unstoppable technological change?