Mapping and the Geometry of Form and Function of Cities - Dissertation Example

? MAPPING AND THE GEOMETRY OF FORM AND FUNCTION OF CITIES The paper analyses the fractal nature of cities for having a deeper understanding of urban density and determinism. Additionally, the aspects of urban boundaries, urban morphology, connectivity, and transportation, node points of the city and hierarchy of connections are discussed in the paper. TABLE OF CONTENTS Introduction 4 Definition and Measurement of Urban Shapes 6 Measurement of Urban Morphology 7 Hierarchy of Connections 11 Mapping, Connectivity And Transportation Within The City 12 Human Activity Towards Different Node Points Via The City 13 Shape, Complexity And Forms Of Cities 14 Urban Design Strategy for the City of Derby……………………….16 Conclusion 19 References 21 Introduction Comprehensive theoretical relationships which form a link between urban evolution, density and location are the basis for the development of all the contemporary models related to urban structure and dynamics. However, these models fail to address the very issues related to urban form. The development of these contemporary models does not take into account the urban development geometry. Instead, these are developed at an aggregate level. Batty and Longley (p. 72, 1994) comment ‘The best way to begin describing fractals is by example. A coastline and a mountain are examples of natural fractals, a crumpled piece of paper an example of an artificial one. However, such irregularity which characterizes these objects is not entirely without order and this order is to be found in fractals in terms of the following three principles. First, fractals are always self-similar, at least in some general sense. On whatever scale, and within a given range you examine a fractal, it will always appear to have the same shape or same degree of irregularity. The 'whole' will always be manifest in the 'parts'; look at a piece of rock broken off a mountain and you can see the mountain in the part. Look at the twigs on the branches of a tree and you can see the whole tree in these, albeit at a much reduced scale.’ Although, it has been observed that there is an acceptable level of consistency between such models and urban form but when it comes to the geometrical considerations of urban development, these are not dependent upon the processes and mechanisms (Bertuglia et al, 1987). The urban system models which are theoretical in nature, like the urban economics models, have shown a dependency upon the urban form through a set of assumptions. However, urban form has been defined by these models in terms of treating urban space as quite simple (Thrall, 1987). Hence, building a model which links a given form to statics and dynamics is very difficult because the relevance of form is considered as given and not something that arises out of the forces in action. As a consequence of this, all the research that has been conducted in urban form is considered to be highly idiosyncratic. However, as a result of some major developments during the last decade the science of form has seen some significant changes, especially within the areas of mathematics and physics. These developments have been brought about by the requirement to establish a connection between urban form and growth processes. In addition to this, another driving force has been the analysis of natural forms on the basis of the occurrence of the geometry of the irregular. Remarkable developments in the area of computer graphics have initiated the mathematical description and visualization of the urban forms. Making use of mathematical principles on fragmented structures, visualization has achieved a milestone (Mandeibrot, 1983). The developments have come about in terms of simulating natural forms (like landscapes) in a simple, yet realistic manner. This majorly involves addition of fractal ideas to produce simulations which are more conventional. This gets further deepened into theoretical ideas which involves the generation of fractal structures through physical processes. The physics of critical phenomena is responsible for the development of a new approach to form modeling which mainly involves the addition and growth of particles of form. As early as the 1980s, there has been extensive use of computer simulation models to produce forms which have an appearance similar to a cluster of various particles. These forms also exhibit self symmetry which is spaced out over a wide scale range along with the structure being subjected to the laws of scaling which are in consistency with the fractal geometry ideas. The diffusion process about a seed particle can be used to generate some of the most articulate and clearest of examples, provided that such diffusion happens on a regular lattice embodying the seed. Collectively, these very models are known as DLA or diffusion limited aggregation models and were first proposed by Witten and Sander (1981; 1983). The structures thus arising out are quite familiar in the form of dendrites or tree-like forms which grow out of a seed. Also, there is a manifestation of self-similarity of these forms over a wide range of scales, with the scaling properties pointing towards their being fractals. Definition and Measurement of Urban Shapes There has been a postulation of three hypotheses with regards to the urban boundaries, related to changes in their fractal dimensions. The first hypothesis states that over a range of scales, boundary exhibits a multi fractal nature. The second hypothesis states that as the scale increases, there is a likelihood of a decrease in fractal dimension. This is because a greater level of control can be exercised over physical development in case of smaller scales. The third hypothesis states that with time, there should be a tendency of the small scale fractal dimensions to decrease because of the institution of more control in areas like land development and building technology. However, when it comes to larger scales, the occurrence of changes in fractal dimensions are not very clear but factors like accessibility and increasing mobility suggest that it will also decrease with time. Batty and Longley (p. 7 , 1994) state ‘Planned growth appears more man-made in that the patterns produced are more regular, reflecting more control over the natural landscape, and the mobilization and coordi­nation of much larger quantities of resources devoted to the development in question. In history, such planned developments are invariably centered upon the areas of towns associated with political or religious power - pal­ace and temple complexes, or with rapidly developing colonial towns, while in the modern age, retail and industrial developments in contrast to residential display some of the same regularity. However, it is impossible to identify solely organic or planned towns, for these two classes of devel­opment merge into one another in many different parts of the city and at many different scales.’ These hypotheses have undergone a process of testing based on the fractal dimensions of Cardiff’s urban boundary in 1886, 1901 and 1922. The times were so chosen because during these periods the population of the city increased from a mere 80,000 to 230,000, thus resulting in rapid urban growth. Additionally, this period also witnessed the developing of tramway system which got initiated in 1872 and culminated in 1914. Also, suburban housing system replaced the predominantly styled housing of the late Victorian worker, thus giving way to more space. Measurement of Urban Morphology Regardless of the manner in which urban analysis is carried out, at some or the other stage cities will be visualized according to the geometric forms. Special terms are taken as a basis to predicate transportation, urban economics and social structure. Hence, the effects arising out of this theory are mostly expressed in terms of geometric factors like urban land use and its shape along with its spread. The most important elements which help in defining morphology are shape and density. These also help in measuring the manner in which urban space is occupied. Until recent times, the relationship between formal theories which explain densities and the geometric form of cities has not been easy to establish. Due to this reason, the economic theories of urban form have developed in a highly idealized geometrical setting which shares a very weak relationship with real spatial patterns. However, it has been observed that the spatial systems like cities are clearly relevant to the development of fractal geometry which is also known as the geometry of the irregular. The fractal theory of cities now shows existence in the most elementary form which has the ability to generate a number of ideas from location theory involving spatial form (Batty and Longley, 1994; Frankhauser, 1994). For more than a century, the urban theory propagates the notion that a self-similarity can be observed across cities, in terms of their functions. This notion finds its manifestation with regards to certain important relations like the rank size rule, the differentiation of service centers based on their hierarchy like in central place theory, the hierarchy of transportation and their various modes and in the area of hinterland along with different orders and their importance (Arlinghaus, 1985; 1993). During the initial years of the building up of a city, the government laid down a particular system of transportation. Urban morphology is an outcome of this system. Later on, certain changes were introduced in this transportation system, which in turn lead to modifications in the structure of a city. In current times, exclusive car cities (before building anything, the network of roads and infrastructure are legislated) are laid down by the governments, or an existing pedestrian city will be destroyed so as to convert it into a car city. In the latter case of destruction of pedestrian cities, some remnants of urban life may be provided by the surviving pieces of the old system (but there will be nothing left if the state machinery is highly efficient). Batty and Longley (p. 56, 1994) quote ‘The term morphology was first coined by Goethe in 1827 as 'the study of unity of type of organic form' (noted in March and Steadman, 1971). Morphology is thus the study of form and process, growth and form, form and functions and as Goethe stated: "The formative process is the supreme process, indeed the only one, alike in nature and art" (quoted in Whyte, 1968). Form too is always more than shape, and we will follow Whyte (1968) who speaks of spatial form which he defines as comprising external form or visible shape, and internal form which is structure. This brings us back full circle to the idea of form being some manifestation of system with structure being the underlying or invisible form which explains the external urban form, the form which is the subject of our immediate and casual observation. Systems are often studied in terms of their statics or their dynamics, the first implying structure, the second behavior usually in the context of changing structures. Our first grasp of systems, at least those that in some sense are external to us, are in terms of their structure from which we proceed to infer their behavior in the quest to understand their dynamics. In fact, it is system structure of which form is the most superficial characteristic which often provides the basis for classification, the begin­nings of scientific study through appropriate description and measurement.’ At times, cities might even resist such drastic changes due to philosophical reasons as reorganization might mean that their growth codes (corresponding to their genes) have undergone a change. However, many cities across the world did become successful in getting transformed from an initial pedestrian city into a car city by changing their genes. Hence, in principle, it is very much possible to undertake the reverse process. Although, the literal meaning of “fractal” is “broken”; in mathematics, this word has an entirely different meaning. A fractal is characterized by very precise properties and is usually out of the understanding of non-mathematicians. Possession of structure on a scale hierarchy is the most important element of a fractal. Another point pertaining to this is the continuation of hierarchy all the way down, as per scales. For instance, corresponding to n=6, one can find around 20 thousand structures (urban spaces, buildings, green spaces) having size 21 m. Moving down the scale, corresponding to n=8, there is a prediction of 531 thousand structures (bushes, components of architecture, street furniture) having size 2.3 m. further down, n=12 will correspond to 387 million structures (natural details and architectural ornamentation) having size 2.8 cm. This process can obviously be taken down to sizes 1 mm and below. Hierarchy of Connections Some new and exciting possibilities for urbanism are offered by the internet (Castells, 1989; Drewe, 1999; 2000; Graham and Marvin, 1996; 2001). It leads to the replacement of many connections which were considered “dirty” because of the enormous amount of infrastructure and fuel that went into feeding them. Although, it has still not been possible to realize the dreams of certain techno-urbanists of the complete replacement of physical transport with the system of electronic tele-commuting, there has indeed been a mergence of the electronic web with the transportation network. In this kind of a situation, paradox of the contemporary city comes into play-all possible efforts are made to remain connected (either virtually or by car), but when it comes to physical connection on the pedestrian scale, that still remains unachieved (Dupuy, 1991; 1995). Nevertheless, as lengthy car journeys get replaced by electronic connections, more value is imparted to a pedestrian city, but we tend to lose out in many other places. Batty and Longley (p. 61 , 1994) state ‘The classic example in the city relates to those routine functions such as retail and commercial services whose frequency and scale of provision is closely tied to the same characteristics of the places where they locate. The largest focus is the CED, while a loose hierarchy of centers exists throughout the city with lesser numbers of district centers, larger numbers of neighborhood centers, even more local centers and so on, with a size and spacing com­mensurate with their position in the hierarchy. The same structure exists for the educational and leisure system which is differentiated according to the finer grained differences between functions.’ Majority of the urbanism problems find their roots in scales. Connection on all scales is a necessity of every city. Different scales correspond to some particular type of connections which are very different in nature. Additionally, since a plane surface or ground level exhibits path wise connectivity of the most economical nature, there will be a competition between different types of connections (Dupuy, 1991; 1995). It is important for a city to maintain balance between all the connections. Like any other competition problem, the connections which are larger or stronger will enjoy a certain advantage over the ones which are smaller or weaker, thus displacing them naturally. The requirement of small scale connections by the pedestrians on ground level is based on the existence of fundamental reasons of psychology and physiology. Unless protection is provided, those paths face serious risk from networks which are much stronger. Mapping, Connectivity And Transportation Within The City A careful observation shows that the establishment of large scale connections is strictly in accordance with their hierarchical position. If one fails to understand this, the appeasing of transportation forces will result in building up of more superhighways, thus erasing lower levels of the hierarchy of transportation (Dupuy, 1995). Complete re-building of pedestrian city into a protected network can happen (Krier, 1998). In order to gain efficiency, the transportation network in many contemporary cities has erased the lower levels in a misguided manner. There is a demand for instantly accessible expressways, built right next to commercial sits and homes. The hierarchies of connections which fall below the highest scale are often skipped. Today, building of highways and widening of low and intermediate capacity roads is happening on a large scale. Of course, there is continuous growth in the city and number of cars, soon to exceed any temporary capacity. Constant up gradation of transportation network is senseless as it leads to the destruction of smaller scales. Human Activity Towards Different Node Points Via The City Connectivity essentially in terms of the topology of connections was described so far. For most part of the discussion, the length, breadth and curvature of paths does not really matter. As per the distribution of sizes, each path is bound to satisfy some distribution according to its dimensions. Now, a talk regarding length of links is necessary so that a connection hierarchy can be established on the basis of geometry. Similar results have been discussed below with the only difference being in the progression from smallest scale to the largest scales. In the urban context, dynamic growth of a town from a village and losing its small scale connectivity corresponds to this progression. To regain the initial connectivity, spatially separated regions can be connected by means of short-cuts. A growing city demands larger roads. Adjustment of communication infrastructure to attain inverse-power hierarchy is the driving force of a network. This is the reason behind the evolution of medieval cities. The same reasons hold good for the modernist city to take a turn towards long connections, was not a realistic planning strategy. The modern city was replaced by car city which has many parking lots due to the requirement of many car trips the city requires. People do not use their car to drive only for travelling between their residence and their workplace for which the drive runs through garden suburb. The usage of car has changed and people use it for every minor movement they have to do. With the cars starting playing major roles in the movements, people are becoming more dependents on the cars and we are expecting connectivity by road to every urban center. This demand is so strong that it is giving rise to a more commercial area due to which the urban area is diminishing. Shape, Complexity And Forms Of Cities The network of public mobility inundates subway, trains or street cars and light rail all got invented owing to this demand during the 19th century. The long routes demanded making shorter routes between the countries in which people lived. The solution that was most feasible was superimposing the transport lanes so that the active walker lanes, vehicle lanes including the primitive transport modes like motor and horse drawn vehicle lanes were not disturbed. Keeping this in mind, the new lanes were constructed either as sub-ways or as flyovers. The metro which connected the populated areas of the city also can be categorized as pedestrian network. The places get better connected and made closer by introducing a few long lanes. There is an expression of unhappiness when a sub-way is introduced. But a little knowledge of the need and idea behind the construction of sub-way would eradicate this unhappiness caused by introduction of sub-ways in car cities. The mere existence of the sub - way in Paris, and post-war commuter suburbs with an already present path for cards, it is not realistic to expect a 19th century European urban populace will progress around the sub-way. This has not happened. The attention in a car city is for addressing the need to provide parking space nearer to a metro station. The other requirements which are required for development of a pedestrian hub are not found and this absence may stop the development of a pedestrian network from being formed here. Despite the above facts, there is much activity around such settings. If the right opportunities are provided, the low scale connections can be achieved almost continuously. The prerequisite for this is supported, directions and restraint to make sure a logical form which is part. The majority of the top-down intrusion brings down the existing infrastructure. The planning should be done keeping in mind the way the urban fabric grows and manages itself, though top down planning is essential. The life in a city is mainly based on the way it is connected (Dupuy, 1991). Every planning is done to ease the connective web which in turn enables more people to interact with each other. Primarily this is the main reason behind people choosing to live in cities. There is a necessity to debate the connective properties of random graph to acquire some knowledge about how city life crops up (Salingaros, 1998). The primary thing that is required to be known is how connectivity is established. Every connection gets established to carry out an interaction amongst any two centers (Castells, 1989, Meier, 1962). This news may be programmed in goods. This can be explained with an example wherein a man wants to travel from his residence to office. The residence and office which are different nodes have to be connected. There should be a presence of a lane to connect these two nodes failing which travelling will not be possible. The centers will connect by means of paths in a non-figurative way. Assume that there are no existing connections. Two centers at a time are connected by selecting them at random which may result in providing link between two centers where the path already exists. This gives rise to an important result, owing to Erdos and Renyi, which shows that after some centers being connected more than 80% of the centres will get connected suddenly (Barabasi, 2002). This is the result of formation of many connected nets of centers, which increase with each step. At the threshold shown by Erdos and Renyi, the nets which were separate, gets connected to form one bigger net, which provides links to most of the centers (Salingaros, 1998). Urban Design Strategy for the City of Derby The city of Derby is mainly based on its minor architectural scales. This invariably includes the ‘detritus’ which modernism wants to discard – misaligned and crooked walls, worn off paint, steps, sidewalk tree, some wall to lean against, places for sitting down and so on. There was an invitation to destroy the decoration which emerged from the Anti-Fractal movement of the 20th Century. Architectural designs are an inherent part of the whole city and relieving Derby of this would destroy one section of the city’s scales. Such methods will eliminate the levels in the urban ladder within the scales 1 mm to 1m. Shortly, structures which held urban space like buildings from 1 m to 3 m which includes kiosks, seating places, gazebos, short walls and so on were eliminated. Finally the sidewalks and the walker lanes of close by buildings were eliminated. The pedestrian city brings in some good things and plus points which can counterbalance the positive points of Derby including an emotionally nourishing physical environment. There is a visual treat and virtual movement, the charm and vibrancy of a lively city, with various populations belonging to a wide age range filling up the sensory stimulation from urban space. The urban life needs an associated network of pedestrian urban spaces, the size of which obeys an inverse power allocation. Many pedestrian lanes are harbored and guarded by open and partially enclosed urban spaces. Both are interdependent. The hub of urban space corresponds with the supports the hub of pedestrian paths (Krier, 1998; Salingaros, 1999). The designing of urban spaces is not done in accordance with the wish of the people who want to spend time with, and the built up urban spaces are completely disassociated with the pedestrian hub, which means the two are totally independent. This change in the concept is intentional which has elicited by applying a straightforward geometry which is not attuned with urban space, and also Derby’s discrimination against the concept of urban space (Saligaros, 1999, 2001b). Systematic connectivity is not dependent on the distribution of sizes. As an example of our ruined cities, consider the existing distribution and connectivity of green areas. People in Derby consider it trendy to grow ornamental greenery like lawns and bushes in places which are not useful otherwise. Though it appears to be good at first glance, the place goes waste with the space being taken off from the pedestrians. This is because they are not connected with each other. They provide the aesthetics which are good to look at for the car city, but totally unconnected to the pedestrian city, which may not exist at all. The existence of green spaces of various dimensions, in an inverse power allocation will not help in creating a network – the first important thing is they have to connect on the human range of scales. Building a pedestrian city in Derby through the transformation of a post war car city is not an easy task as a completely new pedestrian network needs to be rebuilt into the car city. The transportation web of a city forms the basis for determining urban morphology. In case one faces a city that is dysfunctional, the effectiveness of innovative planning cannot be established unless significant changes are made in the infrastructure and the network of transportation. Incorporating such huge changes in Derby is not easy along with being highly expensive. The network of transportation has a larger dependency on connectivity than speed. In order to establish connection with the urban fabric, narrower and smaller streets are required. Most of the cases observe them as being reintroduced as woonerven (semi-pedestrian roads which are narrow and limit vehicle speed). The connection of nodes through long and short links defines a “small-world” network (Barabasi, 2002; Salingaros, 2001b). Beginning with the nearest-neighbor interaction nodes, some longer links can be added at random in the city. This will greatly improve the overall connectivity. When any two nodes are chosen randomly, the number of links between them measures connectivity. If only nearest-neighbor connectivity exists, then all the intermediate nodes will have to be considered. Connectivity can be improved by adding a few longer connections. In this manner, only nearest-neighbor connections get transformed into inverse power path distribution. Conclusion The cities during the 19th century thrived on providing a connector interface between the natural world of plants, bushes, rocks and the constructed buildings. This could be attained using geometry. This concept is not present any more. A greenery is an essentially fractal structure, which does not gain a place into the modernist machine geometry. Anti-Fractal approaches are becoming more obvious as to how the structure is disconnected from the greenery. This has given rise to an un-natural geometry in the natural world. The demand of the modernism is a neatly cut lawn and bush which have a neat cubicle shape. Putting a tree in a square planter is a coincidence of two incompatible geometric figures. It is evident that the urban morphology is decided by how the city’s transportation net is spread. All the planning will not work until and unless the transportation network and the infrastructure are elevated. This is not an easy option to carry on and also it takes a lot of funds. Cities may not be willing to make such radical changes for the philosophical reasons since it involves shift of the codes of growth in resonance with their genres. The majority of the cities worldwide have been successful in changing their genes to develop a car city from the existing pedestrian city. This ensures that it is possible to do it the other way as well. Batty and Longley (p. 364, 1994) state ‘Fractal geometry has emerged in direct response to the need for better mathematical descriptions of reality, and there is little doubt that it pro­vides a powerful tool for interpreting and rendering natural systems. Yet in its wake has come, once again, the realization that all knowledge is con­tingent upon its context in time and space, that good theory is relative to what we already have and have had before, thus reminding us of Einstein's (1921) thoughts on the limitations of any geometry, indeed of all mathemat­ics. Although extending our abilities to model both natural and artificial systems, fractals impress even further upon us the inherent complexity and uncertainty of the world we live in. In this sense, one kind of uncertainty -that involving the inapplicability of Euclidean geometry to many real sys­tems - has been replaced with another - a more appropriate geometry for simulating reality, but one which is based on the notion that reality itself has infinite complexity in the geometric sense.’ The present urban regeneration diverges into two different problems. One is how to breathe life into car city and the second is how to energize the non-living pedestrian inner cities. The solution for the first is to build a pedestrian hub within the car city, eliminating little of it in the process. This can be attained without imposing restrictions on the car / truck network. Connectivity can still exist. The second case connected to the slum is not easy to handle because of the social problems which combined healthy mixture of urban functions which describe a living city. The people living in a slum are disassociated from others owing to the crime rate, drugs, literacy level and skills. The people of slum do not have the long scale social connection for interactive information transfer. References Alexander, C. (1965) "A City is Not a Tree", Architectural Forum 122, No. 1, pages 58-61 and No. 2, pages 58-62. Translated into many languages. Reprinted in: Design After Modernism, Edited by J. Thackara, Thames and Hudson, London (1988) pp. 67-84. Published electronically by RUDI (2001) http://www2.rudi.net/bookshelf/classics/city Alexander, C., Silverstein, M., Angel, S., Ishikawa, S. & Abrams, D. (1975) The Oregon Experiment, Oxford University Press, New York. French translation: Une Experience d'Urbanisme Democratique, Editions Seuil, Paris, 1976. Alexander, C., Ishikawa, S., Silverstein, M., Jacobson, M., Fiksdahl-King, I. & Angel, S. (1977) A Pattern Language, Oxford University Press, New York. Spanish translation: Un Lenguaje de Patrones, Editorial Gustavo Gill, Barcelona, 1980. Barabasi, A. L. (2002) Linked: The New Science of Networks, Perseus Publishing, Cambridge, Massachusetts. Batty, M. & Longley, P. (1994) Fractal Cities, Academic Press, London Castells, M. (1989) The Informational City, Blackwell, Oxford. Drewe, P. (1999) "In Search of New Concepts of Physical and Virtual Space", paper presented at the Conference: Cities in the Global Information Society: an International Perspective (University of Newcastle, Newcastle-upon-Tyne, November 22-24, 1999). Published in: M. Schrenk, Editor, Beitrage zum 5. Symposion "Computergestutzte Raumplanung" -- CORP 2000, Volume 1, Vienna University of Technology, pages 37-44. Drewe, P. (2000) "ICT and Urban Form: Planning and Design Off the Beaten Track", Delft University of Technology, Design Studio 'The Network City', Faculty of Architecture. Dupuy, G. (1991) L'Urbanisme Des Reseaux, Armand Colin, Paris. Dupuy, G. (1995) Les Territoires de l'Automobile, Anthropos, Paris. Frankhauser, P. (1994) La Fractalite des Structures Urbaines, Anthropos, Paris. Graham, S. & Marvin, S. (1996) Telecommunications and the City, Routledge, London Graham, S. & Marvin, S. (2001) Splintering Urbanism, Routledge, London Kauffman, S. (1995) At Home in the Universe, Oxford University Press, New York Krier, L. (1998) Architecture: Choice or Fate, Andreas Papadakis, Windsor, Berkshire, England. French translation: Architecture: Choix ou Fatalite, Norma, Paris, 1996. Italian translation: Architettura: Scelta o Fatalita, Editori Laterza, Roma-Bari, 1995. Meier, R. L. (1962) A Communications Theory of Urban Growth, MIT Press, Cambridge, Massachusetts. Mikiten, T. M., Salingaros, N. A. & Yu, H. S. (2000) "Pavements as Embodiments of Meaning for a Fractal Mind" Nexus Network Journal 2, pages 61-72. Reprinted as Chapter 7 of A Theory of Architecture, Umbau-Verlag, Solingen, Germany, 2006. Salingaros, N. A. (1995) "The Laws of Architecture from a Physicist's Perspective", Physics Essays 8, pages 638-643. Salingaros, N. A. (1998) "Theory of the Urban Web", Journal of Urban Design 3, pages 53-71. Reprinted as Chapter 1 of Principles of Urban Structure, Techne Press, Amsterdam, Holland, 2005. Finnish translation: "Kaupunki Verkostona", Tampere University of Technology, Institute of Urban Planning, publication No. 33 (2000). Salingaros, N. A. (1999) "Urban Space and its Information Field", Journal of Urban Design 4, pages 29-49. Reprinted as Chapter 2 of Principles of Urban Structure, Techne Press, Amsterdam, Holland, 2005. Salingaros, N. A. (2001a) "Fractals in the New Architecture", Archimagazine, approximately 6 pages. Traduzione in italiano: "I Frattali Nella Nuova Architettura", Archimagazine (2001), circa 6 pagine. Salingaros, N. A. (2001b) "Remarks on a City's Composition", RUDI -- Resource for Urban Design Information, approximately 14 pages. Reprinted as Chapter 5 of Principles of Urban Structure, Techne Press, Amsterdam, Holland, 2005. Finnish translation of the first half: "Kaupunki ei todellakaan ole puu", Yhteiskuntasuunnittelu -- The Finnish Journal of Urban Studies 39 (2001), pages 68-76. Salingaros, N. A. & West, B. J. (1999) "A Universal Rule for the Distribution of Sizes", Environment and Planning B 26, pages 909-923. Shorter version reprinted as Chapter 3 of Principles of Urban Structure, Techne Press, Amsterdam, Holland, 2005. Read More