The simplicity of planar networks

Shortest paths are not always simple. In planar networks, they can be very different from those with the smallest number of turns - the simplest paths. The statistical comparison of the lengths of the shortest and simplest paths provides a non trivial and non local information about the spatial organization of these graphs. We define the simplicity index as the average ratio of these lengths and the simplicity profile characterizes the simplicity at different scales. We measure these metrics on artificial (roads, highways, railways) and natural networks (leaves, slime mould, insect wings) and show that there are fundamental differences in the organization of urban and biological systems, related to their function, navigation or distribution: straight lines are organized hierarchically in biological cases, and have random lengths and locations in urban systems. In the case of time evolving networks, the simplicity is able to reveal important structural changes during their evolution.Comment: 8 pages, 4 figure

Geospatial analysis and living urban geometry

This essay outlines how to incorporate morphological rules within the exigencies of our technological age. We propose using the current evolution of GIS (Geographical Information Systems) technologies beyond their original representational domain, towards predictive and dynamic spatial models that help in constructing the new discipline of "urban seeding". We condemn the high-rise tower block as an unsuitable typology for a living city, and propose to re-establish human-scale urban fabric that resembles the traditional city. Pedestrian presence, density, and movement all reveal that open space between modernist buildings is not urban at all, but neither is the open space found in today's sprawling suburbs. True urban space contains and encourages pedestrian interactions, and has to be designed and built according to specific rules. The opposition between traditional self-organized versus modernist planned cities challenges the very core of the urban planning discipline. Planning has to be re-framed from being a tool creating a fixed future to become a visionary adaptive tool of dynamic states in evolution

Cities as emergent models: the morphological logic of Manhattan and Barcelona

This paper is set to unveil several particulars about the logic embedded in the diachronic model of city growth and the rules which govern the emergence of urban spaces. The paper outlines an attempt to detect and define the generative rules of a growing urban structure by means of evaluation techniques. The initial approach in this regards will be to study the evolution of existing urban regions or cities which in our case are Manhattan and Barcelona and investigate the rules and causes of their emergence and growth. The paper will concentrate on the spatial aspect of the generative rules and investigate their behaviour and dimensionality. Several Space Syntax evaluation methods will be implemented to capture the change of spatial configurations within the growing urban structures. In addition, certain spatial elements will be isolated and tested aiming to illustrate their influence on the main spatial structures. Both urban regions were found to be emergent products of a bottom up organic growth mostly distinguished in the vicinities of the first settlements. Despite the imposition of a uniform grid on both cities in later stages of their development these cities managed to deform the regularity in the preplanned grid in an emergent manner to end up with an efficient model embodied in their current spatial arrangement. The paper reveals several consistencies in the spatial morphology of both urban regions and provides explanation of these regularities in an approach to extract the underlying rules which contributed to the growth optimization process

On the right track? : evaluation as a tool to guide spatial transitions

Spatial developments are becoming more and more non-linear, dynamic and complex with a wide range of possible actors. The awareness of uncertainty in spatial planning is growing and therefore, projects need to integrate a high level of flexibility. But at the same time, a growing demand for taking more informed and well-argued decisions is noticeable. Predictions out of the ‘best estimated model’ are no longer credible and no longer accepted, because they are too fragile and uncertain. How can we keep these long-lasting, multi-actor projects in permanent transition on the right track? This article presents an evaluation methodology that goes beyond the traditional, rational evaluation attitudes with a low level of flexibility being too linear to match the current spatial developments. There is a need for more interrelated, alert and flexible means of evaluation, co-evolving with the processes and current dynamics in spatial planning. Therefore, different evaluation approaches are introduced, depending on the specific interdependencies of the object of evaluation and its context. Subsequently, the theoretical framework is translated towards a more practical level. A case study conducted in Flanders illustrates the current spatial developments and a possible evaluation approach, incorporated from the beginning of the process, to guide this kind of projects

Can geocomputation save urban simulation? Throw some agents into the mixture, simmer and wait ...

There are indications that the current generation of simulation models in practical, operational uses has reached the limits of its usefulness under existing specifications. The relative stasis in operational urban modeling contrasts with simulation efforts in other disciplines, where techniques, theories, and ideas drawn from computation and complexity studies are revitalizing the ways in which we conceptualize, understand, and model real-world phenomena. Many of these concepts and methodologies are applicable to operational urban systems simulation. Indeed, in many cases, ideas from computation and complexity studies—often clustered under the collective term of geocomputation, as they apply to geography—are ideally suited to the simulation of urban dynamics. However, there exist several obstructions to their successful use in operational urban geographic simulation, particularly as regards the capacity of these methodologies to handle top-down dynamics in urban systems. This paper presents a framework for developing a hybrid model for urban geographic simulation and discusses some of the imposing barriers against innovation in this field. The framework infuses approaches derived from geocomputation and complexity with standard techniques that have been tried and tested in operational land-use and transport simulation. Macro-scale dynamics that operate from the topdown are handled by traditional land-use and transport models, while micro-scale dynamics that work from the bottom-up are delegated to agent-based models and cellular automata. The two methodologies are fused in a modular fashion using a system of feedback mechanisms. As a proof-of-concept exercise, a micro-model of residential location has been developed with a view to hybridization. The model mixes cellular automata and multi-agent approaches and is formulated so as to interface with meso-models at a higher scale

Elementary processes governing the evolution of road networks

Urbanisation is a fundamental phenomenon whose quantitative characterisation is still inadequate. We report here the empirical analysis of a unique data set regarding almost 200 years of evolution of the road network in a large area located north of Milan (Italy). We find that urbanisation is characterised by the homogenisation of cell shapes, and by the stability throughout time of high-centrality roads which constitute the backbone of the urban structure, confirming the importance of historical paths. We show quantitatively that the growth of the network is governed by two elementary processes: (i) `densification', corresponding to an increase in the local density of roads around existing urban centres and (ii) `exploration', whereby new roads trigger the spatial evolution of the urbanisation front. The empirical identification of such simple elementary mechanisms suggests the existence of general, simple properties of urbanisation and opens new directions for its modelling and quantitative description.Comment: 10 pages, 6 figure

On the problem of boundaries and scaling for urban street networks

Urban morphology has presented significant intellectual challenges to mathematicians and physicists ever since the eighteenth century, when Euler first explored the famous Konigsberg bridges problem. Many important regularities and scaling laws have been observed in urban studies, including Zipf's law and Gibrat's law, rendering cities attractive systems for analysis within statistical physics. Nevertheless, a broad consensus on how cities and their boundaries are defined is still lacking. Applying an elementary clustering technique to the street intersection space, we show that growth curves for the maximum cluster size of the largest cities in the UK and in California collapse to a single curve, namely the logistic. Subsequently, by introducing the concept of the condensation threshold, we show that natural boundaries of cities can be well defined in a universal way. This allows us to study and discuss systematically some of the regularities that are present in cities. We show that some scaling laws present consistent behaviour in space and time, thus suggesting the presence of common principles at the basis of the evolution of urban systems