Sociology has brought forth two antithetical models of the city: the concentric "Chicago" model and the polycentric "Los Angeles" model. In this presentation I revisit these models through the lens of linear and nonlinear mathematical modeling. I show that the concentric model can be described with linear mathematics while the polycentric model requires nonlinearity. My presentation also traces the distinction between linear and nonlinear modeling across a broad array of sciences and summarizes what type of observations can be described with linear and nonlinear modeling respectively. Linear models are best at describing predictable change, evolution, and progress. Nonlinear models are required when it comes to interplay between multiple diverse parties and chaotic behavior that is hard to predict. For architects, these insights may be particularly intuitive to understand. A straight line looks straightforward, while curves are more frequently associated with playfulness. The presentation will fit the present conference topic, as it is a discussion about urban models and about order and linearity versus disorder, playfulness, and nonlinearity.

Recently, minister Hugo de Jonge presented a sketch for the new spatial planning act in the Netherlands. The underlying idea ‘Netherlands as a whole’ implies developments should not primarily take place in the lower clay soils of the Randstad but also in the peripheral regions of the Netherlands. According to Joks Janssen, this narrative offers opportunities for strengthening the Zandstad, referring to the agglomeration of cities on the higher sand-soils in the east and south. In the last years, various visions for the Netherlands already hinted in this direction. Interestingly, there’s already a steady flow of people moving to the east. This is primarily explained as the expansion of the Randstad itself, but there is also a slow and steady number of people moving to the ‘far east’–the peripheral regions de Jonge is referring to, on the sandy soils. This steady flow of people already presents regional and local governments with a dilemma. To strengthen the liveability, they welcome (modest) growth. But they also want to maintain the regional and local identity – which might come under pressure. We conceptualize this identity issue as a multi-scale phenomenon resulting from both the spatial distribution of cities, towns, and villages and the impact this has on the motivation and behaviour of its inhabitants. We do so from the perspective of complexity theories of cities (CTC) and by using the concept of urban regulatory focus. The latter is a recently developed concept of urban complexity and dynamics that links city size to humans’ motivational behaviour. According to regulatory focus theory, a person’s goal-directed behaviour is regulated by a certain combination of two motivational systems, promotion and prevention. Individuals who are more promotion-oriented focus on winning and tend to take risks, whereas those driven by prevention goals tend to focus on not losing and try to avoid risk. According to urban regulatory focus, one’s personal regulatory focus is both dependent on one’s chronic regulatory focus and on the urban environment in which one lives. Bigger, fast-paced cities polarize both motivation and behaviours, while smaller, slow-paced cities encourage more moderate and less polarized behavioural responses. In the paper we explore the question of what happens if this shift from core to periphery in The Netherlands becomes more substantial. We do so by playing City Games as a new methodology: participants from the Randstad and Zandstad with differences in personal regulatory focus interact to create scenarios for accommodating growth in the east. By playing these games and analysing the outcomes we aim to answer the question on how the shift from Randstad to Zandstad might impact the regional and local identity – supporting decision-makers now and in the future.

The systemic approach and complexity theory now allow the city to be interpreted as a dynamically complex system in which each element is interacting with the others. This makes it complex to jointly evaluate the phenomena related to the different subsystems that can be identified in the urban system: the socio-anthropic subsystem, the geo-morphological subsystem, the functional subsystem, and the physical subsystem. Such an assessment is necessary to optimize the use of resources in the policies and the actions of the government of urban and territorial transformations from a sustainable perspective. Data from the Global Footprint Network highlight how resource consumption is increasingly high and rapid and does not allow for the regeneration of resources for the planet’s annual needs and, in a broader sense, for the needs of future generations. This study aims to identify an integrated paradigm for the analysis and monitoring of urban systems based on the concept of "systemic entropy," which enables to identify, in a georeferenced manner, the urban areas characterized by major dyscrasias, for which policies and intervention actions can be appropriately developed. Based on the interpretation of the city as a "dynamic dissipative system" elaborated by Ilya Prigogine and on the extensive scientific literature that has followed, an experimental methodology has been developed that allows us to highlight critical issues for each urban subsystem while assessing its level of systemic entropy. Systemic entropy is defined as a measure of the state of disorder or degradation of the urban subsystem (or the whole system), generated by the misuse of resources and which can be traced to a general condition of "unsustainability." The procedure linearly combines normalized values related to a number of entropy indicators. These indicators are also elaborated with reference to the numerous studies in the literature about indicators of urban sustainability in its three key areas: social, economic, and environmental. The procedure developed was tested on a specific urban context, the Fuorigrotta neighbourhood in Naples. On that specific urban context, the procedure made it possible to highlight the most entropic areas, to define the causes and to develop a ranking based on the priority of intervention needed. As for the steps of the procedure: first, entropy indicators were calculated for each subsystem; then the values related to entropy levels, the results of which informed the creation of a decision support tool that can guide decision makers and administrators toward the implementation of integrated sustainability-oriented strategies. In conclusion, the study highlighted the potential of a method for defining systemic entropy in the development of operational decision support tools for public administrations that can optimize the use of resources to foster sustainability-oriented urban problem solving.

The authors of the paper discuss the challenges faced by cities in monitoring and evaluating sustainable development. With the increasing availability of data, cities are faced with the challenge of keeping track of a large volume of metrics and indicators. The use of "Ideals" can help unite actors in pursuing important goals and provide a shared interpretation of concepts used. However, the lack of a bigger strategy behind the collection of existing monitoring frameworks in the city of and the absence of compatibility between different datasets and indicators can result in siloed ways of working. The authors suggest the use of Ideals to bridge disciplines and achieve more holistic insights through the use of indicator-based monitoring systems. Therefore, the development of a domain ontology is proposed to integrate existing urban datasets and monitoring systems with the values or ideals a city promotes. The paper utilizes the city of Amsterdam as a case-study for this approach, but eventually puts forward an open-source model that can be used by other cities.