Contemporary Religious Architecture. Between Concept and Identity

Religious Expressions of Chicanos in Los Angeles. From the body to the streets. In Between Concept and Identity. Edited by Esteban Fernández Cobián. Cambridge Scholars Publishing, UK. PP 163-169. 2014. ISBN (10) 1-44386520-6. ISBN (13):978-1-4433-65203

I'm happy to say that this paper of mine has been published in a compiled edition of the Symposium Between Concept and Identity, that was held in Spain in 2009:

" the Ourense Bishopric through the Santa María Nai Foundation and the Ourense Branch of Galician Official Association of Architects (COAG) have called a new edition to be held from November 12 through 14, 2009 in Ourense under the title: Contemporary Religious Architecture. Between Concept and Identity."

This is my introduction:

I propose a sub-classification within representational spaces, full of complex symbolism and usually related to the underground side of life: there is a third space or Nepantla, applied to the culture of Mexican immigrants in the USA and their descendants, popularly called Chicanos. They create this new space from the feeling of being in the middle as a cultural link among Anglos, Mexicans and Indigenous people. Nepantla is considered to be a transitional stage that simply starts with language. One of the cultural settlement strategies is precisely the process of trans-culture acquisition and value transfer, which is summarised in a different culture reflecting the ambiguity of mixed race. Once the Nepantla tensions are understood and faced, the native Being/I is recovered and thus Nepantla becomes a psychological, spiritual and political space where Chicanos find the meaning of their culture by recovering the ancestral. Those religious spaces range from bodily artistic expressions to the materialisation of traditional little altars at home and it is expanded to the urban scale, to worshipping the dead and to Catholic rites in the street where both the harmoniously co-existing Catholic and pagan imaginaries give rise to massive gatherings. Therefore, we must analyse the religious expressions of Chicanos as an unavoidable part of their social reality in the city of Los Angeles portrayed at every possible scale. Due to their own restrictive colonial origins, they do not need a containing building but are merely supported by faith.

The link to buy the book:

http://www.cambridgescholars.com/between-concept-and-identity

Buenos Aires: Urban quadrille and fractality under the light of social aspects

This is a personal translation of Buenos Aires: cuadrícula urbana y fractalidad a la luz de aspectos sociales. Published in Spanish in the Proceedings of CONGRESO FFRACTARQ, España 2004
The following text in English has been published in:
Proceedings, 4º International Conference of Mathematics and Design, 2004. Special Edition, vol. 4, No 1. Buenos Aires. Urban Quadrille and Fractality Under the Light of Social Aspects. ISBN 950-29-0823-6

Lea el original en español:

http://urbanfractality.blogspot.com/2012/07/buenos-aires-cuadricula-urbana-y.html

ABSTRACT

Investigations about urban form are developed in many directions, being the history branch the strongest. It is based on the importance of forms created for previous generations. So, urban morphologists must examine the inhabitants and the processes that origined the urban form. In our discipline, ´´Epistemological Physicalism´´ is studied through the theory of complex systems and chaos theory. The resultant shape is obtained by selecting some elements of the abstract structure considered (non Euclidean geometry) and simulation software is used for experimentation, like L Systems, Difussion Limited Aggregated, Cellular Automata. Then we have to discover what is veiled at first sight and reflected in the optimal model for the community.

INTRODUCTION

The concept of experiment presupposes the existence of a theory, without theory there would not be experiment, only observation. The term "theory of the architecture" suggests a scientific domain of the architecture whose intention resides in providing from dependability to the theoretical foundations of the discipline. 

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

The investigations on urban form are continued in many addresses, being the historical branch the strongest, based on the importance in the ways 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. The prevalence of the model of Physics ("Epistemological Physicalism"), from a reduccionist conception, would not be a correct way to carry out an investigation. 

In our discipline, the Epistemological Physicalism is studied through the theory of complex systems, under the theory of the Chaos. The resultant formal product is achieved by selecting some elements of the considered formal abstract structure (Non Euclidean geometry: fractals) and the experimentation is carried out by means of simulation softwares as L Systems, Difussion Limited Aggregated, Cellular Automata.  However, the results obtained, need of our intuition and experience for an appropriate selection; then we will meditate which the appropriate pattern for a certain collectivity is. 

The rules preset in the software urge us to the "search of the truth" starting from diverse patterns, we could find what at first sight is hidden. In this process, this technology is an useful experience of thought.  

THE CASE OF BUENOS AIRES

The form is relative to our record of it. We could suppose, for example, that planned cities, - where the man imposes his geometry on the environment - are typically Euclidian, but this posture is not verified when we change the scale again: in a satellite photograph we find that the processes of social dynamic urban growth, denote extremely irregular borders; we come closer and when observing the urban fabric, the Euclidean patterns of the original layout disappear (read it as a limitless grid, a drawing in the land that ignores the geography of the place), and we only see a three-dimensional fabric similar to a fractal.

In first instance, for an approach to the case of Buenos Aires, we could refer to professor Pierre Frankhauser's works in the scientific aspects of the block morphology (1). Then, we will try to demonstrate, why Buenos Aires is presented like an atypical case and it needs to be understood with a reflexive, interdisciplinary attitude that allows us deviations and divisions in the investigation.

Frankhauser settles down that the mensuration methods based on the fractal geometry, allow us to verify to what extent the patterns of the real world show the hierarchical organizations and where the ruptures of the same ones take place. For it, he starts from the most elementary characteristics in the spacial distribution of built areas. The convenient modelization is the Sierpinski Carpet, generated by iterations. The professor warns us on the results of the fractal dimension, since they reflect the hierarchical organizations in a global way, according to the number of their elements and not their position, which will be of supreme interest if it is compared to the "lagoons" (patios, parks, squares). He also highlights the importance of carrying out mensurations through the time, to evaluate the dynamics in the pattern's formation.

We could deduce that the analogical pattern of the  Sierpinski carpet would be applied to any urban conformation that is originated in a quadrille(2). however, the pattern based on the Sierpinski carpet  does not reflect the pattern of Buenos Aires in the barrio scale , because its morphogenesis has been different to that of the European cities, due to geographical, social, political, economic causes. The paradox resides in that Buenos Aires was inhabited fundamentally by European. (3)

For experimentation, we have taken a typical block of the neighbourhood of La Boca del Riachuelo, in Capital. The mensurations of the fractal dimension according to the box-counting method has a value that reaches 1.80 (4). But, as professor Carl Bovill notices in his book "Fractal Geometry in Architecture and Design", this dimension does not take into account the overlappings. 

The empiric observation accuses this question: under the roofs, we find intermediate spaces, covered, semicovered spaces that superimpose in floor plans and in elevations, a fabric of diverse materiality, crossed by pipes, clothes, cables that enclose even more the block heart and leaves an extreme complex fabric.

HISTORICAL CONTEXT AND MORPHOGENESIS

In 1580, Juan de Garay carried out the second foundation of Buenos Aires, in the vicinities of the Riachuelo de las Conchas, that assured appropriate water depth to the ships. The layout of the future city, was carried out based on the Indian American system, a grid of 15 front blocks by 4 at the bottom. The appearance was rather a regulator design, where the low density forms of semi-rural organization were dominant in the open fabric, including housing and vegetable garden until advanced the SXVII. It is necessary to clarify that although the old maps define the streets, the spatial habitat was very different, since the streets were of mud and they conformed a continuum with the wetlands and the streams. That is to say, the block did not morphologically exist, except in old plans.

The first dwellings were organized around patios, according to those of Andalucia, and according to the  "Pompeyan" type, also with successive, nested patios. The urban trace is reaffirmed in 1608, and although it had a clear structure, the precariousness of the settlement made the residents to settle in disorder, invading adjacent lands, forcing the Municipality (Cabildo) to exercise the control of the buildings development. Architect Jorge Liernur attributes it to the widespread uncertainty, the previous stadium to a consolidated project. By the middle of the S.XVIII some  precursor forms of the tenant houses were already known, and it was a common habit to share the big family housing  with several tenants and temporary guests.

In the census of 1744 there are already housings inhabited by 33 people, counting family, servants and tenants (see Jorge Páez, 1970). With the fall of Rosas in 1852, Argentina begins a process of "modernization and reorganization", where the immigrants contribution occupies a fundamental place. As an example, it is enough to affirm that in 1661-1870, 159.570 immigrants entered the country; between 1881-1890, 841.122 entered, between 1901-1910, the number ascended to 1.764.101. The contingents were composed of Italian in their majority, Spaniards, French, Englishmen, Swiss, Austrian, German, Belgian, Turks, and others in non significant number. An unexpected phenomenon of growth and urban expansion took place, and it generated a problem of accumulation and tugurization caused by the massive occupation of the old dwellings and the emergence of the rental houses, then denominated "conventillos".

The conventillos consist on the grouping of cells (rooms), attached to the division walls (medianeras) that had already begun to appear, with a long corridor that served from the entrance to the patio, which in turn contained the kitchen and to the back, the common toilet. The growth of cells is given by aggregation (5). We illustrate this concept with the synoptic table of three properties of ends of S.XIX, located in La Boca, carried out by Marcelo R. Morales and Horacio A. Paradela in their report "Conventillos. La Boca. Integration, manipulation and conflict" (Faculty of Philosophy and Letters, University of Buenos Aires1999. Unpublished).

Curiously, the society, independent of the many nationalities it is composed, also grows by aggregation: at first, a few immigrants settle down, and then, on time, they keep on slowly bringing their closest relatives.

This aggregation is not reduced to the domestic dwellings, but also to the industrial buildings and in consequence to electrification.

  “...la introducción de motores eléctricos aceleró la proliferación y el crecimiento de pequeños establecimientos....Analizando la planta de Piccardo en 1908, no se registran signos de ningún proyecto o plan que pueda haber presidido su evolución; al contrario, parece haber crecido por  agregación....Pequeños locales estancos se mezclan con locales amplios...Esta variedad y la irregularidad tipológica que causaban los sucesivos crecimientos eran permitidas sobre todo por la ubicuidad de las fuentes de energía”. (Liernur y Silvestri, in “El torbellino de la electrificación”, El Umbral de La Metrópolis. Buenos Aires, 1993).

¨....the introduction of electric motors accelerated the proliferation and growth of small settlements…Analyzing the floor plan of Piccardo in 1908, there is no record of signs of any project or plan that could have preceded its evolution; on the contrary, it seems to have grown by aggregation… Small fixed rooms are mixed with ample rooms…This variety and the typological irregularity that caused the successive growth were mainly allowed for the ubiquity of the energy sources¨. (Author´s translation)

And advancing in the text, corresponding to Artifacts, he also explains that ¨ “...la forma por agregación de los artefactos se hacía hegemónica sobre el resto del ambiente...” (… the shape for aggregation of the artifacts was being hegemonic on the rest of the ambiance…¨.)(Author´s translation).

 Amos Rapoport sustains that the domestic architecture shows its compositive character  clearly: "buildings inside buildings", he even considers the furniture and the fire like a primordial type of "building" of independent evolution; it is possible to arrive to the scale of the  material component, its texture, etc. This spacial organization is similar to that of a fractal pattern. The self similarity does not verify  in the partial forms of our urbanism, but in the infinite succession of identical patterns that  goes from the macroscale to the microscale.

Let us observe a typical house of the neighborhood of La Boca: it is usually said that the forms achieved by the carpenters coming from the South of Italy, resemble to their native houses and they give the barrio the "italianizante" identity. However, we must consider that by the time of their construction (SXVIII-SXIX) the isolated housings, built in wood and zinc sheets proliferated in Buenos Aires, for their quick execution and the available materials: wood, zinc sheets, disassembled parts of ships (6), remains of demolitions like doors and old windows, tiles, etc. Obviously, we are before a true culture of the fragment that did not have to do with the immigrant cultures, but with the consequences of the exercise of the political power, rescued in the ideologies of hygienists and the real estate speculation. An invisible, omnipresent power that evolved to materiality thanks to the sacrifice of its victims, the conventillos inhabitants, that lived crowded and  died in quantity for the ferocious epidemic of yellow fever in 1871, that attacked mainly in the poorest neighbourhoods closer to the Riachuelo. ¨Cities -- at least the most pleasant ones -- are fractal. Everything, from the paths and streets, to the shape of façades and the placing of trees, is fractal in the great cities ……. Colonnades, arcades, rows of narrow buildings with cross-paths all correspond to a permeable membrane with holes to allow interchange -- this is one type of fractal.¨ (N. Salingaros, “Fractals in the new architecture”)

LAST CONSIDERATIONS ON THE ANALOGIC MODELS AND THEIR APPLICABILITY

Of what is previously exposed, it comes off that the applicability of the analogical pattern is not to include all the cities with similar morphological patterns, and that it will vary according to the period in which one works. We have seen that the plans do not reflect the spacial vivences, and they should only be taken as starting points.  

It will be looked for, therefore, appropriate modelizations of the tendencies in urban growth. A preliminary proposal for the modelization of urban dynamics in Buenos Aires – in the Barrio scale -, divided in three chronological periods, could be:

·        Applicable models to dispersed, granular fabrics, with use of "noise" filters for a better evaluation of the contrast among built and vacant areas. The mensuration of the fractal dimension would correspond to the graphs of noise.

·        Aggregation models that reflect the morphogenesis of blocks. The iteration models would be optimal in the study of parcel subdivisions, product of real estate speculations at the end of SXIX.

·        Models that show major urban fabric openings, based on the Urban Planification Code, (Analogous to the Zoning Code) that states for a typical block, not to exceed with constructions the 25 meters, counted from the property line, in order to leave an empty block heart. The investigations show that the current tendency in free perimeter tower construction, generate openings in the compact urban fabric, with which the blocks would be defined again by the property line, at the edge of sidewalks. Maybe in a near future, in many neighborhoods, the optimal modelization would be the one based on the city´s origins, supported with 3 dimensions, due to the diversity in heights. In our experimentation, we worked we Cellular Automata, beginning with compact configurations taken from aerial pictures from SXX. The results simulated the fabric dispersion, similar to the one at SXVIII, and to some modern barrios where low houses conglomerations are built adjacent to the free perimeter towers. This research is still in process.

From the sociological-historical study we conclude that in our multi ethnic society, there was no spatial disaggregation of collectivities, but they were melting in one along the years, a Babel tower which phenomenom makes it very hard to define the cultures of the first collectivities separately, through the architecture and urbanism. The identity has been achieved in their iconography, mystics aspects, food, music, aesthetic details. Actually, the current urban fabric of Buenos Aires is so complex, very irregular in its volume, in spite of the rigid trace of its quadrille. It expresses a way of life, the social plurality, the back and forward steps in politics and economy, the advance of spontaneous popular fabrics in contraposition to the strict rules in the ¨Center¨. This is what makes of Buenos Aires an atypical city, and quoting architect Clorindo Testa, what is interesting, when opening a window, we do not know what we will see, with which landscape we will meet…..

 BIBLIOGRAPHY

Bovill, Carl. Fractal Geometry in Architecture and Design. Design Science Collection. Birkhäuser. 1996

Bucich, Antonio. Cuadernos de Buenos Aires VII, “El Barrio de La Boca. La Boca del Riachuelo desde Pedro de Mendoza hasta las postrimerías del siglo XIX”. Municipalidad de Buenos Aires, 1970

Censo Municipal de Buenos Aires del 17 de agosto de 1887. Tomo II. Museo Mitre. 1887

Clementi, Hebe. Protagonistas de La Boca...un pueblo. Instituto Histórico de la Ciudad de Buenos Aires. 2000

Frankhauser, Pierre. “Fractal Geometry of Urban Patterns and their morphogenesis”, en Discrete Dynamics in Nature and Society, Vol.2, pág.127-145, Université de Franche-Comté, Francia, 1997.

--“The Fractal Approach. A new tool for the spatial analysis of urban agglomerations”

Gutiérrez, Ramón. Buenos Aires. Evolución Histórica. Talleres Gráficos de Escala. 1992

Liernur, Jorge F. y Silvestri, Graciela. El Umbral de la Metrópolis. Transformaciones Técnicas y cultura en la modernización de Buenos Aires (1870-1930). Colección Historia y Cultura. Ed. Sudamericana. Buenos Aires, 1993

Morales Marcelo R. y Paradela Horacio A. “Conventillos. La Boca. Integración, manipulación y conflicto” (informe para la Facultad de Filosofía y Letras, Universidad de Bs. As, 1999. Inédito).

Páez, Jorge. El Conventillo. Colección Grandes Exitos. Centro Editor de América Latina. Buenos Aires, 1976

Planos de Buenos Aires Siglos XVIII, XIX y XX. Museo Histórico de la Ciudad y Biblioteca de la Facultad de Arquitectura, Diseño y Urbanismo.

Rapoport, Amos. “Aspectos Humanos de la Forma Urbana. Hacia una confrontación de las Ciencias Sociales con el diseño de la forma urbana”. Colección Arquitectura/Perspectivas, Ed. Gustavo Gilli, Barcelona, 1978

Salingaros, Nikos. Fractals in the New Architecture, Archimagazine. Ed. on line

Spinadel, Vera. Microcurso “Fractales, Caos y Diseño Urbano”. (ICVA-1º Congreso Virtual de Arquitectura).FADU, Argentina, December 1999 to January 2000.

NOTES

(1) Refer to “Fractal Geometry of Urban Patterns and their morphogenesis”, in Discrete Dynamics in Nature and Society, Vol.2, pág.127-145, Université de Franche-Comté, Francia, 1997. Also  “The Fractal Approach. A new tool for the spatial analysis of urban agglomerations”. In these scholar papers, the closest example to Buenos Aires is the city of Besancon (patrón D=1.81)

(2) In 1997 Frankhauser reports 20 metropolis analized at regional scale, based on fractal patterns, mainly European. The research in the microscale have begun in the last years, being its precursors Batty and Xie, who are supported by American data resources “Tiger” y GIS.

(3) The reference is strict for the planned city, we are not referring to the Indigenous population that in Buenos aires have not constituted cities by settlements, as the Quilmes.

(4) The methodology was adopted following the premises of professor Carl Bovill, given that the external figure that contains the boxes is a rectangle. We consider that the rectangle adjusts to the majority of blocks and their profiles, giving this way more accurate results than the option of square as an external figure. The dimension in autosimilarity includes the superimpositions, that is why we adopt it in mensurations of cross sections and urban profiles (urban plots).

(5) The term calls out to fractals classified as  DLA (Difussion Limited Aggregation), due to their analogy with the particles in a solution, attracted by an electrod.

(6) The possibility of utilizing ships as a first dwelling, and-or their parts, is suggested by archaeologist Marcelo Weissel, in “Había una vez un puerto”. El puerto en el Riachuelo y la Arqueología del Rescate. Produced by the Instituto Histórico de la Ciudad de Buenos Aires. 1998

URBAN MORPHOLOGY AND FRACTAL DESIGN

(Published in Spanish in Contextos 11. Personal translation)

ABSTRACT

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.

INTRODUCTION

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.

HISTORY IN THE URBAN MORPHOLOGY-COMPLEX SYSTEMS RELATIONSHIP

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

http://homepages.rpi.edu/~eglash/eglash.htm

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.

DESIGN AND COMPLEX SYSTEMS

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.

COMPLEXITY THEORY

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.

RELATION OF FRACTALS WITH CHAOS THEORY

"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.

ANALYSIS OF DYNAMIC SYSTEMS AND VERIFICATION OF THE RESULTING URBAN MORPHOLOGY

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

FINAL REFLECTIONS

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

 REFERENCES

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