Urban society is undergoing as profound a spatial transformation as that associated with the emergence of the industrial city two centuries ago. To describe and measure this transition, we introduce a new theory based on the concept that large-scale, complex systems composed of many interacting elements, 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-organized 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 which find expression in fractal geometry and weak chaos theory. We illustrate the theory using a unique space–time series of urban development for Buffalo, Western New York, which contains the locations of over one quarter of a million sites coded by their year of construction and dating back to 1773, some 60 years before the city began to develop. We measure the emergence and growth of the city using urban density functions from which measures of fractal dimension are used to construct growth paths of the way the city 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 threshold since the emergence of the automobile city some 70 years ago. Our implied speculation is: how long will this kind of urban form be maintained in the face of seemingly unstoppable technological change?