Cities as complex systems: notes on the dynamics of urban evolution

Pondering on cities as complex systems in general; the way their morphological and functional aspects are in continuous change, we see cities come up with new and unexpected spatial and functional patterns. Urban planning in its contemporary form can organize and attenuate the results or the tendencies of urban processes which arise from social metamorphoses. Yet, often, procedures inflected by planning to move the events in a certain direction often fails to accomplish that for more than short periods of time after which it may lead to undesired or even opposite results. This is because our knowledge of the complex nature of the urban system is still insufficient to formulate a new approach to planning that is truly effective and efficient as a tool to ''negotiate'' spontaneous processes. So, what we need is a deep understanding of what is going on in our cities which are being transformed so fast and whose transformations are but a surface change hiding a much bigger number of changes and processes touching virtually everything from (among others) social networks to movement patterns to land prices to many small physical and functional changes which go unnoticed. The sophistication we discern in the city is similar to that in many natural and man-made systems which we might call complex, and any attempt to imagine it would fail if it is not based on an explanation which is valid for all these systems; from here rises the core of this research which relies on a thorough investigation of complexity theory in an attempt to understand cities as complex systems. Thus the main objectives of this research are to try answering these questions: How do the diverse ''components'' of the city come together to make up urban evolution? What are the dynamics of the incessant urban change in all its forms? In such a complex system, is it possible to identify the real processes acting at the local scale but causing transformations at the global scale? Yet, identifying real processes at work at many levels of complexity and at different scales is inseparable from studying resulting geometric patterns, therefore, another fundamental objective of this research is to gain insight into how form and process are intertwined. The apparent complexity and the reality defying planning and outweighing it, all mean that the problem of urban complexity should be confronted in an interchangeable method which has its roots in various other fields, such as: complexity theory, dynamical systems and topology. The research methodology is about exploring those fields and highlighting their interconnections with the concept of complexity in general and later arguing deep similarity with the urban case. Constructing abstract representative models is at the heart of the research in complexity; cellular automata (CA) and multi-agents simulations (MA) are the main simulations used for exploring complexity. It is argued that the computer-aided simulation is a kind of representation which has the ability to reflect a non-linear process, this research introduces a different method than pure representation, which is to approach complexity from all possible directions while benefiting from the conclusions reached by simulations. We proceed by giving an in-depth investigation of complex systems in general, by discussing their universal phenomena such as: catastrophic events, fractals, ''oneover-f '' noise, power laws, punctuated equilibrium, and self-organized criticality. Along with a focus on their abilities of self-organization and of reaching a sophisticated kind of order through their own internal logic even if their initial conditions were no more full homogeneity or extreme randomness; this order is usually achieved and maintained by forming large-scale patterns. Therefore, complexity theory shifts the emphasis of research from studying independent variables into to interdependent variables; a dynamic rather than a static conception. It also concentrates on extracting the fundamental mechanisms of all complex systems, such mechanisms are themselves intricate and not easily discerned. Reading present ''mutations'' in cities in general, we attempt to discern a prevailing pattern. Cities, nowadays, continue to loose their historic cores as they continue to spread making the physical form of the future city will take unclear. Therefore the currently prevailing mutation pattern is one that is at the global level, but the real changes take place at the local level. Urban change in general occurs through relocation of activities which usually causes chain-reaction effects which range from small into catastrophic urban changes. As suggested by the self-organized criticality's proponents, the duration and size of activities involved in such chain reactions follow power laws. We also study the dynamic relation between rates of change of the physical reality of the city on one hand and its body of functions on the other, in addition the relation between the rate of change of the city as a whole and its elements taken individually. This detailed study acts as an adaptation of the theory of self-organized criticality to the urban case. Which is further enriched by incorporating the influence of the movement networks in cities on its dynamics, that is, the tendency of the structure of the grid itself to be the main influence on the pattern of movement. The Core of the study and its most lengthy chapter is an elaboration of all previously discussed concepts and ideas along with conclusions derived while carrying out the discussions. We take off, in this part, first by focusing on some individual urban evolutionary processes by drawing insights from computer-aided simulations, thus, a bunch of example models (which are based on discovering very simple local rules) by various researchers are discussed, this includes Edge city model, Urban potentialdevelopment model, Active walker model, sugar-scape model and urban growth pattern according to critical thresholds model. The conclusions from those models creators are then further analyzed. Thereafter, this research reaches its kernel when it becomes possible to identify the individual ''concepts'' which are the correct keys to the problem the basic of the basic and thoroughly explore them. The attempt is to frame the elusive notions of structure, order, network, hierarchic organization and morphogenesis especially from a topological point of view. And deriving conclusions about the issue of process and form through defining the kinds of ''shape changing processes'' which have complex spatial consequences. An attempt to frame the important concepts of structure, order and structural stability in complex systems especially those with specific spatial manifestations; thus, a discussion about the difference between the notion of a ''network'' to that of a ''structure'' is outlined, and an investigation of the detailed interdependence between order and structure is carried out, pointing out that it is the structure which takes precedence rather than order in determining the existence of the other. Structure as a concept is compared to the notion's of rules and sequences in computer systems since a relationship gives a fundamental to the following step or relationship and since the order in which the rules appear can drastically change the overall outcome so this directly implies a global kind of process; finding a global solution to fit in the relations in question so that they keep existing and in the process also support each other, an example is the deformed wheel pattern of roads found in self-organized cities. And it is argued that structural stability is determined by the way the structure has been created, that it is inherent in the structure itself rather than as it may seem dependent on external factors. The understanding of structural qualities in cities is linked to morphogenesis and the recognition of the dynamics created by space itself, and here morphogenesis is used as the basis to distinguish true generative processes working in reality to create form. In order to evolve the previous discussion, two particularly interesting characteristics which cities often exhibit are investigated, namely: the rank-size rule of cities (zipf's law), and fractal structure. The reason behind the appearance of Fractality in urban spaces is a key in understanding their complexity, therefore it is studied under its connection to:1. morphogenesis because in all cases, the notion of scaling is directly connected to that of fractality, and 2. the notions of density and chain reactions arguing that not only that fractality reflected in density and its capacity limits is connected to the location with respect to the center, but, more importantly, the nature of fractality is connected to, or rather, is influential on the extent of the chain reactions in cities. One of the most important issues in understanding the form-process problem is that related to energy, it is natural for things in general to seek the situation with the least potential energy, therefore, finding the best ''shape'' that is the shape which will result in the least potential energy is crucial for the systems functioning. In selforganized cities there is a quality of ''optimization'' that is always sought and preserved through the city's evolution, this quality provides us with a clue relating self-organized urban structure, its stability and the principle of minimization of energy. We argue that alongside feedback mechanisms the network is also experimenting new solutions (that includes new or modified focuses, and new or modified forms). We argue that the fundamental mechanism by which this happens in cities is very similar to that which creates a natural river network. The optimization principle is also considered from a topological point of view, realizing that mere saving in distances and better connectivity throughout the system are not of the utmost importance. We point out that topology tells us a relevant lot about shapes and energy through the various embedding domain of existence types of forms. Thorough considerations are presented about the relatedness of the prevailing pattern of diffusion in present-day cities in most parts of the world on one hand and self-organized criticality on he other, through presenting the concept of fluctuations in the complex system which generates the system's stability. Some considerations are made about the patterns of cluster formation in cities by summarizing some of the cluster-growth issues as: Expansion at the global level such as expansion of the urban fringe or many expansions of component clusters. The study then explores the important similarities between the urban phenomena and general phenomena studied by physics centering on the morphological transition in urban form. And links that to transitions in fractal dimensions in cities over time, together with the key notion of the shifting from direct growth to indirect growth in cities. And to strengthen the suggestions of this line of thought a further investigation of the aggregation as mechanism for organization in complex systems is presented supported by concepts about the dynamics accompanying such mechanisms namely, the anticipation mechanisms in a complex systems while explaining the concept of genetic algorithms as a useful tool in our study. A point in our study is reached where an exploration of ''form'' is needed, thus, a discussion about form and morphogenesis from a dynamic point of view is presented as a key concept in an effort to sum up threads from all the concepts and theories previously presented. Keeping in mind that what is meant by form is not the mere physical appearance, architectural styles or geometric details, what is more relevant is the quality of the interlock between solid and void (built and open space), the general configuration, arrangement and succession of open spaces and the ''dynamic'' quality of form types. The reasoning starts by some exploration and criticism of the rules of the Bottomup models under the guidance of an understanding of the notion of form. Arguing that state of the art cellular automata models, and multi-agent models and the like seem to accurately represent important mechanisms, the mechanisms themselves, nevertheless, seem to be linear and give an impression of lacking the more intricate complexity we deal with in the city. Based on this argument, the study suggests a modification to such models in order to incorporate those effects, by making use of some topological concepts; such as topological manifolds and vector fields. The study then proceeds to the central argument in understanding ''form'' which is the ''problem of succession of form''; as addressed by René Thom studying morphogenesis from the point of view of topology, tracing not shapes but processes which occur in infinite-dimensional spaces. The key point is that it is a method which puts emphasis above all on the morphogenesis of the process, that is, on the discontinuities of the phenomenon. The study thoroughly investigates the general topological model proposed by Thom in order to parametrize the local states of a system and deriving an interesting ''definition'' of an object and how every object is characterized by its domain of existence; an idea which is important in our quest to understand embedding of local in the global in a dynamic way. And from there the mathematical notions of form, nonform, structural stability, maps and topological equivalence are reached. key idea here, is that the stability of a form is directly determined by its position in relation to the basins of attraction of the dynamic, so a first step in considering the stability of forms is composing the general attraction mechanisms of the dynamic system. An attempt is presented as to how to see urban forms in the light of these definitions and discussions, and an analysis is argued to be based on characteristics of its global, local and intermediate scales. The study concludes by highlighting the necessity of a multi-disciplinary and non-linear approach, because, as the flow of the study shows, each of the conclusions reached at each section is derived from either concepts from various disciplines or from a purely logical argument or from both, that's why though such conclusions might not look connected, they are threads which do not aim to a single point, but rather aim at knitting a whole intact foundation for a new form of urban sciences, a form that relates their current form with the ambitious science (and philosophy) of complexity theory.