| Abstract: | We present an analysis of the effects of different information flow patterns on the growth of spatial structure in a broad class of systems. Examples are drawn from plant and message diffusion processes, the growth of herding in animal populations and, in particular, the evolution of cities in human populations. We model the actions of an “individual” as a response to gradients in a transformation of the “real” space, this transformation being the individual's information map of the space. Interesting deductions occur as a result of allowing the individual's information map to vary from extremely local to extremely global. In the city growth model for example, if migration decisions are based upon extremely local information, then the system is characterized by instability and the lack of any well-defined spatial structure. As the localness of this information map decreases, the system is characterized by the development of well defined spatial structure with a characteristic distance separating the “cities.” In a particular case, we show that the wavelength of the dominant spatial structure is directly related to the size of an individual's information field. These effects are a consequence of interactions between individuals that arise from the nonlocalness of the information fields. We interpret the early growth stages in these models in terms of linear filters. |
