Cities and Regions as Self-organizing Systems: Models of Complexity

In a beautiful novel, the Argentinian writer Jorge Luis Borges `quotes' a Chinese saying `̀ dejo a los varios porveniresöno a todosöeste jard|̈n de senderos que se bifurcan'' (`̀ I leave to the various futuresönot to allöthis garden of forking paths'') (Borges, 1994). The solution to the detective novel lies in the nature of the garden and of his labyrinth: the forks happen in time, not in space; therefore several possible futures are created, each qualitatively different from the others. This is the first, persistent issue in Allen's work: the statementöfull of consequences for anyone who deals with modelsöthat `̀ there is a critical difference between asking whether a system obeys the laws of physics or whether its behaviour can be predicted from a knowledge of those laws'' (page 2). That leads to the conclusion that `̀ We cannot really predict, but we can explore possible futures, and can help to imagine some of the properties of these'' (page 258). Complex systems, as everybody knows, are very sensitive to initial conditions andöat some stages of their evolutionösmall changes in their variables are enough to produce big, structural changes: `̀ ... history is made up of successive phases of relatively predictable development along a particular branch, separated by moments of instability and real change during which the future of the systems is laid down by some rather indeterminate chance events which push it onto one or another branch'' (page 18). Urban systems add to the unpredictability of all complex systems, another element, namely the fact that `̀ ... people interact and ... their `utilities' are linked in a complex, co-evolutionary fashion'' (page 3). In short, people often do what they want and estimate the different choices not necessarily on the basis of a rational and constant reasoning, but often according to sensations and opinions which depend on other people's choices and their changing sensations and opinions. For model builders this fact has important implications for the type of models that should be used and the purposes for which they could and should be used. The second issue in the book lies in the definition and presentation of a large and wellgrounded series of models that Allen describes as `̀ Self-organizing models''. A self-organizing model is essentially a type of model which ``should somehow generate the structure of today, from among other possibilities, and hence would be capable of examining the future without supposing that today's structure would continue forever''. It recognises `̀ through time, the relevant classification will change, and the variables, and their attendant equations will also change in different phases of the development of systems'' (page 20). These characteristics are presented at different levels of refinement in two theoretical examples, one which reexamines the classic central place model and one on a Lowry type of model, as well as in several applications to actual cases of interurban evolution (long-term structural changes in the USA; spatial evolution of jobs and people in Belgium; an evolutionary model for Senegal which also integrates the environmental factor) and infraurban evolution (applied to a town like Brussels). The models presented are able to comprehend also the qualitative elements of actors' behaviour when calculating `̀ an `ideal', latent potential for a given choice. The dynamics of the system is driven by the difference between the observed, revealed pattern of choice at a given time, and the value of the ideal ... the dynamics results from movement towards a moving target. This is a key difference between this approach and others which assume, or are calibrated, so that revealed behaviour defines preferences, and change is simply modelled as a quasi-equilibrium process of instantaneous adjustment to exogenous changes in some parameters'' (page 232). It is worth pointing out here the differences between self-organizing models and those based on system dynamics, which are deterministic and whose zoning structure is predefined and does not emerge from the model's evolution and those commonly used (the twelve models Reviews Environment and Planning A 2000, volume 32, pages 1325 ^ 1330