Sunday, August 5, 2012

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:


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.


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 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.


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.
  “ 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 ¨ “ 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”)


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…..


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.


(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

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