Tuesday, July 31, 2012


(Published in Spanish in Contextos 11. Personal translation)


The cientificism as a model of the science on accuracy and logical-formal perfection has been and it is the tool that allows us to find the order inside the chaos, detaching the pure, neutral science,  of all religion and ideology.  

The development of the contemporary science has generated theories that transform our knowledge of the universe. 
These theories are taken by the designers and they are the starting point of the formal exploration of the projects, as  processes of denaturalization.


The professor of urban studies at Rutgers University, Susan Fainstein revises and criticizes three post positivists current models:
1. - Communicative planning: rooted in the  pragmatic American philosophy (with emphasis in the empiricism) and the European critical theory.  
Inside this structure, the primary function of the planner is to listen people's stories and to attend the consent among the different points of view. 
The investigation in the communicational area is based on the aspects of the meetings (encounters).  
2. - The equitative city: it introduces a space model of relationships based on  justness. This thought is fundamentally  followed by sociologists. The intentions are good, but the projectual perspective is scarce.
 3. - The well carried out city: of morphological orientation. It is projected (designed) a desirable city that can be obtained through the planning. It has discussions on the design, the spaces, the suitability of the urban structure. As example we mention the  New Urbanism, inspired on a kind of social movement that reacts to the sprawl (uncontrolled growth ), proposing varied uses inside a neighborhood and a re-order of the traffic, in a substantial interest for the project and not the way of carrying it out. 

The more recent post-positivists developments, have tried to develop the concept of "Good City" , and focus on the principles and strategies that should underlie in the progressive urban social movements. 
Although the thought of the "well carried out city" is the dominant one in our Faculty of Architecture, Design and Urbanism, we conclude that these three thoughts must interact. 

And, if the architects start from a morphological conception in the study of the urban transformations, our proposal consists on not to separate the structure of the processes that give it origin, including the use of interdisciplinary conceptual models that enrich the methodology to study and guide it toward an anthropological conception.


The urban morphology is simply defined as the study of the urban shape, and it can be integrated for several other disciplines. 
Their origin goes back to the tradition of morphogenetic investigation  of Central Europe. The German geographer M. R. G. Conzen, emigrated to England in 1933, established the foundations of the urban morfogenesis in the English-speaking countries, and he applied them to analyze the evolution of the towns and cities of Great Britain. 
The conception of Conzen was innovative, and the most significant in its contribution was the conceptualization in the way in that the urban form is developed. Their tripartite division of the urban landscape in: plane of the town, building forms  and uses of the land, like complex forms related hierarchically, until arriving to the "Cell of the urban landscape",  have been accepted as fundamental advances in the theory. (1)
For the decade of the '60s, most of the studies were not based on the history, the planning of towns and cities it was still based in containers  of the use of land.  Prominent critics of this position are Kevin Lynch, Christopher Alexander and Jane Jacobs who urged for a more human approach to the urban planning. Alexander was the one that incorporated mathematical concepts for the first time in the study of the same ones, understanding that the city was an organized complex in the way of a biological organism that could only be understood by means of new conceptual tools. In this context, C. Alexander writes "A City is not a Tree", where he substituted the  ramified  shape by a reticular complex (lattice), and he demonstrated that this was the only appropriate way to solve the complex problems. He affirmed that all the historical  or "natural"  cities have many overlappings or subsets that imply their diversity. With the development of those "patterns" or outlines, Alexander polished these ideas, and with its work team applied them to the quarters of Peru. Alexander’s methodology still continues effective.

Recently, the study of the urban shape is continued in many ways, being the historical branch the strongest, based on the importance of the shapes created by previous generations. Already, the urban morphologists do not limit their attention to the form, but rather they also examine the individuals, organizations and processes that have led to that form. (2) The investigations that originated on the ideas of Conzen, incorporate the agents involved in the processes of change. In the decade of the '90s the terms "morphological frames" , "patterns" (models) (3), "urban micro-scale" were already  used, all concepts that define a city. The theory of " Fractal City " (Batty and Longley, 1994, Batty and Xie, 1996), demonstrates the origins of the shape of urban fractals, and it implies a direct relationship with these models.
The theoretical application together to the concept of culture of the towns, has as an  antecedent the project of creation of an Indigenous Center for Education and Development in the city of Ziguinchor (Africa), based on the fractal aspects of the African indigenous culture. (1996, Ron Eglash, C. Sina Diatta and E. Onyejekwe). The project began with the observation of aerial pictures of African traditional establishments that demonstrated to have fractal structures (tree structure, rectangular recursive enclosures, circles formed by circles of housings, etc.). Later studies, showed that this fractal architecture was of intentional designs, and that these characteristics could be found in other African cultural areas (art, religion, engineering, games). These results are based on the theory of complexity, and they suggest that the primitive societies took advantage of the non lineal aspects of the ecological dynamic systems.

African Settlement with fractal morphology and morphological  study in its culture. Courtesy Dr. Ron Eglash

The new theoretical positions are in frank opposition with the modern urbanism; it establishes that the most pleasant places are fractals:  
 "Everything, from the roads and the streets, to the form of the facades and the location of trees, is fractal in the big cities like Paris, Venice and London.….. Colonnades, arcades, lines of narrow buildings with crossed roads, everything corresponds to a permeable membrane with holes that allow the exchange - this is a fractal type". (4)

With regard to the urban space, Dr. Salingaros highlights the importance of the perception (especially that of the pedestrian) and the physical contact with the elements that conform the urban space. To more segmentation, it corresponds a bigger information of the urban space toward the individual. Under this concept, fractality in urbanism is demonstrated in the multiple scales: from the city to the material and color of which the facades are made. The floor plan has lost the importance in front of the individual's spacial perception. 
In our point of view, the concept of " fractal city " should be supplemented with the study of the dynamic systems, and the self-organized criticality, this way, we are able to elucidate the underlying socio-cultural processes that led to those forms.  
The dynamic models take concepts of the physics, sometimes direct (Newtonian gravitational attraction) (5) or indirect (balance of markets, competitiveness) and they are appropriate for the research on urban systems, given their grade of impredictibility (6).   From this point of view, mathematics and physics should be described in themselves as innovative processes open to design.


The mathematical theory then contributes to a better understanding of the universe and the complex systems that compose it, for the grade of abstraction that it allows to apply, and, taking as a tool the computer technology, it  allows to open new investigation fields, supplementing imagination and logic. 
The behaviors of the complex systems can be simulated with computers, and in these simulations, they can be good designs through the experimentation between variables of projects and operative conditions.  
Among the appropriate softwares, we mention Cellular Automata, Difussion Limited Aggregated (DLA), Neural Networks, with all their variants.
In the study of urban morphology we find absolute conditions as the site geography, the climate, etc, and other flexible as the economic, political, social. An optimal urban design would take into account all the conditions, what triggers a greater compromise between the designer and the society.


The components - agents - of a dynamic system that interact in their criticality state (when the properties of the system suddenly change) self-organize forming a hierarchy of the emergent properties of the system. This has the ability to come closer to a critical point - limit of the chaos -, and it is there where a small change can push the system to a chaotic behaviour or to maintain it in a fixed behaviour. This postulate suggests a flowing and interconnected world, conceived as a whole, contrarily to the traditional scientific postulates that take the human beings and the nature like individual objects.

When perturbing a chaotic system appropriately, it is forced to take one of the many possible behaviours; we denominate this phenomenon bifurcation. But without sincronism, and under different environmental conditions, two virtually identical chaotic systems, will evolve toward different final states.  
In a system self-organized by individuals, there are several organization levels. The small parts of a system have their own properties; this would be the lowest level in organization. These parts form a block with a next organization level with other emergent properties, and so forth. These levels can have self-organization, as the societies, the organs or be manufactured, as the machines and cars.  
According to the historical context, the population's density, the environmental conditions, etc., the behaviour patterns change; the individual behaviour follows some rules and the collective one follows others. Starting from this,  retro-feedings take place with which the system is self-organized; then the collective rules restrict the individual rules. The complexity of a system depends on the scale in which the system is analysed.  

Self-organization of systems: miners in Brasil; Peruvian barriadas
 Pictures from Google images

Another concept to define is that of self similarity, that is to say the invariance of shape through  changes in the observation scale. The mountainous landscapes have picks of all the sizes, from kilometers toward millimeters. The clearest and simple example is that of the cauliflower: from the complete flower until the last florette that composes it, the structure is the same one. 
And the same phenomena is observed in some towns or cities: as we change the scale, the same patterns repeat.

The city of Guanajuato in México shows a fractal pattern, with obvious self similarity characteristics. Pictures from Google images

To solve problems is the biggest creativity in the human behaviour, and it derives of the brain. This, as an alive system, is autopoietic, that is to say, is self constitutes in a learning system and organization, in which the continuous structural changes take place, while the auto-organization pattern is unalterable. These changes, are consequence of the influences of the environment and they are developed in the structure of each human brain. When different individuals are gathered (different chaotic subsystems) the creativity is increased: each one of them, with its own auto-organized creativity loses some grades of freedom to achieve others that correspond to the collectivity.

"How to transmit to the other ones the infinite Aleph that my fearful memory hardly remembers? The mystics, in similar trance, lavish the emblems: to mean the divinity, a Persian speaks of a bird that somehow is all the birds; Alanus of Insulis, of a sphere whose center is everywhere and the  circumference in none; Ezequiel, of an angel of four faces that at the same time goes to the East and the West, to the North and the South.  (Not in vain I remember those inconceivable analogies; some relationship has with the Aleph). Maybe the gods would not deny me the discovery of an equivalent image, but this report would be polluted of literature, of falsehood. Apart from this, the central problem is irresoluble: the enumeration, at least partial, of an infinite group."

Professor Jorge Luis Borges questions it himself, in the story "The Aleph", written in 1949. The character looks for some representation form for the symbol of the transfinite numbers, an image of the infinite and of the complete knowledge. 
Similarly, fractals represent the dynamic systems, the geometry of the nature, the infinite retro-feedings, in synthesis, what cannot be measured in Euclidian terms . 
The term that in Latin language means fragmentary or interrupted, was presented by the Polish mathematician Benoît Mandelbrot (1924 -) for the first time in their book "Them Objets Fractals: Form, Hasard et Dimension" (1975). 
A fractal has not been defined yet, but its characteristic properties are enumerated: great irregularity, detail in arbitrarily small scales, frequently they present a certain form of self similarity. 
Geometric fractals can be generated in very simple form, in general a recursive one. 

Mandelbrot set, a classic example. Fractal generated with Fractal Explorer 2. By Myriam B. Mahiques

Systems are fractal when at any critical point, a continuous transition phase takes place.

Fractals and chaotic systems have both the property of self similarity.
The chaotic sets have the tendency to develop fractional dimensions.
Summarizing, both concepts, chaos and fractality are complements.


We already count on informatical methods for the study of non lineal systems. The first questions for the analysis of dynamic systems of a town or city would be:

Which are the limits of the system? 
Who are the actors in these crisis? (agents) 
How these actors influence each other? (interdependence) 
How is their behaviour in connection with the environment? (emergency) 
 Which are the external parameters that influence the actors’ decisions? (interferences) 

Which is the structure of organization of the system? (hierarchical levels) 
Which are the social characteristics of the actors? 
Which is the common pattern in the system time and space? (rules) 
We suggest, following the theory of chaos that the use of the conceptual models is carried out to local scale and the prediction to short term. 
The simulations allow us to explore quickly with a computer the numerous initial positions  (pre-established rules) of a system and the emergent results in a lapse of certain time, for then to be able to compare them; for the urban designers, the simulation is a good method to optimize the projects, to avoid crisis and to calculate the environmental impacts.  
The urban design depends on the social context; therefore the designers should work with models that include multiple scales space, multiple actors, multiple objectives, multiple approaches. 
 In Center MAyDI, we have studied historical antecedents, besides those mentioned, the theory of the complexity and fractal morphology is applied to vernacular settlements: we mention as an important example the study of the Mayan cities, Guanajuato, Pueblo Bonito (USA), etc, and when the city is planned, like it is the case of Buenos Aires, in the first place we determine the study scale, to therefore apply the Sierpinski carpet for a detailed analysis of blocks.  

Morphology pattern of Tikal and Pueblo Bonito. Google Images
Aerial picture of a block in Capital de Buenos Aires and Sierpinski carpet- Carpet image from Google images. Collage composed by Myriam Mahiques

Enlarging the scale, we have selected the neighbourhood of La Boca from its origins until ends of 1970, since it has been studied many times in its morphological and ethnic aspects, but they have not been conjugated yet. It is important to point out that in cases of mandatory habitability, the environment becomes a critical element and the survival of the cultures can be determined by the form of the housing and its settlement in the territory. (Rapoport, 1977). 
 Our intention is to establish a new analysis methodology for the professionals that work in urban project and face emergency situations.  

 La Boca, exemplified in successive scales, also shows fractal characteristics and its first inhabitants produced bifurcations in the system, specially in times of the plague. Pictures: personal archives by Myriam B. Mahiques


It is necessary then to wonder, based on the statements above, if the limits marked by the use of the land are accurate for the study of the urban morphology of a settlement, intimately related with the society or if we should reconsider the analysis processes used until the moment. 
These considerations imply a change of the traditional paradigms of the planning, producing an evolution in the models of analysis of urban morphology.  
We propose the following methodology:

1. - Use of the paradigm to control the self-organization processes 
2. - Identification of non deterministic margins as operability fields. For example, we could take regional limits, barrial, ethnic, etc. supplementing with the calculation of their fractal dimension measured in several stages of their growth. 
3. - Establishment of matrix, abstract but commendable forms of different possible developments. The use of the fractal geometry is fundamental for a matrix development 
4. - To advance in the detail scale, verifying the self similarity of the system, by means of the application of the fractal geometry  in blocks, buildings, facades, textures. 
5. - Understanding of the Social  as base of the conformation of the society, applying an abstract pattern that defines it. The empiric data and the theory,  will help to increase the level of understanding of our urban environment.  
6. - Comparison and overlapping of both conceptual models: the one applied for urban morphology and the one applied to define the society. 

Supplementing appropriate softwares for the absolute and flexible conditions, the designer will achieve a bigger social commitment. "The urban contemporary renovation demands technical and different cognitive and social qualities, according with the work on existing structure. To renovate a residential neighbourhood demands to study their history first, the way they work, to listen and to respect the vision of the users, to take their problems and their typological preferences seriously" (M. Welch Guerra, 2002). The identity is inherent to the personal and collective development of a society; for this reason, the designer will work contemplating the cultural expressions, with groups that represent the collective interests, trying to avoid the social alienation.

Arch. Myriam B. Mahiques, february 2003


1.- These concepts are related with the investigation on "urban genetics", in vogue in the last years. This theory leans on the evolutionary characters of the towns and cities, starting from non regularized transformations. It is based on the discovery of the inherent logic of emergent processes in a dynamic system, using computer tools to visualize and to a certain point to predict space and organizational changes in the time. Considering that a model of similar behaviour exists among "urban genes", that is to say a homology among the natural and artificial evolutionary systems, simple norms of self-organization are applied to the model selected, then they transform it, achieving a bigger space complexity

2.- We mention two examples, the first one, a model of development of use of the urban land, based on economic classic theories (Webster & Wu, 1999). In this example, it is important the recognition of the actors’ and of the effective urban market’s behaviour. The rules should represent the way in which the communities, the individuals and the authorities would react before different local situations, always in the search of the well-being. The second example is based on rules of transition of cells (Cellular Robot) where the residential preferences of different groups in a multicultural city are expressed at local level (Benenson, Omer & Portugali, 1999); it is to carry out relocations, optimizing the residential segregation, or analyzing the isolation in that the individuals are living in neighbourhoods of groups to which they don't belong.

3.- The idea of "pattern" implies that the environment has a structure and it is not at random a group of united elements, they reflect the relationships between people and the physical elements. The objects and people are related through a separation in and for the space. (A. Rapoport, 1977)

4.- N. Salingaros, “Fractals in the New Architecture”,
Archimagazine http://www.archimagazine.com/afrattae.htm (translation from the Spanish)

5.- Alvin Toffler, in his book "The Third Wave", writes about the  Newtonian causality: "If the world was composed of separate particles - billiard balls in miniature -, then all the causes came from the interaction of those balls. A particle or atom hit another. The first was the cause of the movement of second one. That movement was the effect of the movement of the first one..... suddenly, an Universe that had seemed complex, disordered, impredictible, richly stuffed, mysterious and jumbled, began to seem neat and orderly". (Toffler, 1980)

6.- In general, these models, when being computerized don't reflect the processes and the real forms exactly, but they are extremely appropriate for the verifications of the same ones inside the urban systems, in a lapse of given time. The computers can suggest imaginative solutions to certain problems by means of the identification of new relationships between people and resources.

REFERENCE: Morfología Urbana y Diseño Fractal, in Contextos 11: Vivir en la Ciudad, p. 30-35, june 2003, FADU.* This book contains also a publication of the famous architect Norman Foster, p.108-113

No comments:

Post a Comment