Evolution From Abstract Expressionism to Architecture

Textil 1.Fractal digital Art with stripes, by Myriam B. Mahiques

As time goes by, it is increasingly difficult to establish the boundaries between the arts and between the arts and sciences. A student of audiovisual design would categorize some superhero movies as "redundant special effects and editing cuts", a child would say that this film is a comic, in its format; the films directed by Peter Greenaway can be seen as plays, books, paintings exhibited in a museum. And architectural objects can be seen as works of art, urban design as both art and manifestations of physical science or mathematics research, based on scientific aspects which results derive from formulas where intuition or social issues do not always take place.

Maybe it is easier to relate sculpture with architecture, as seen in my previous post “Blurry frontiers between art and architecture”, because both of them are tridimensional, and we can also find some roots in collage. But relating optical art, post painterly abstraction, to a three dimension object, is not such an easy task.

By 1950, Abstract Expressionism was at the top of success. The idea was to articulate surfaces of the paintings as “fields”, rather than compose them: the canvas determined the pictorial structure, it was beyond painting. To activate the field, canvas were divided horizontally or vertically by band/s of color. The American artist Morris Louis took this concept to the limit, he worked with unsized canvas and soaked –more than painted- the fabric like dyed cloth, so it became a painting in itself. It was a clear rejection of cubism and sculptures.

Morris Louis painting. www.iu.edu/~ocmhp/062405/text/arts.shtml

Phantom Tattoo, by Jim Davis. blog.art-tistics.com/?m=200805

In 1960, some artists turned to brilliantly colored shaped works (diamonds, semi circles) that activated not the canvas, but the wall surface. There was then a period of experiments with paintings with stripes of different colors, followed by another period of shaped canvases fitted together in series to make serial compositions. The next step was asymmetrical canvases painted in vivid colors which segmented the shapes, some of which were curved. It developed into painted metal reliefs (stripes) attached to the background.

It is interesting to notice that while both Abstract Expressionism and Pop art triumphed in Europe, Post-painterly abstraction did not make an impact in the European scene. Europeans, specially British artists, were different from their colleagues in America in the fact that they remained fascinated by pictorial ambiguity, and continued to play with effects of depth and perspective, technique that was closer to an architectural drawing.

Julian Spalding, in his book “The Eclipse of Art: Tackling the Crisis in Art Today”, highly criticizes the use of such hard geometric patterns. On Bridget Riley’s works, he comments that her stripes “had been applied by a machine”….”Her lines were ruled; …masking tape was used to ensure that the edges were sharp. What had to be eliminated was any hint of human presense”. And then “But where does that lead? If a work of art is not centred on humanity, what is its form? Why stop at the edge of a canvas, when one could cover the whole wall?”.

Bridget Riley, optical art. RA2. http://nadav.harel.org.il/Bridget_Riley/

Now, with fractal art, we do not need the tapes, and yes, we do need a machine: the computer. The example below is a fractal I have generated from a Sierpinski triangle, and it looks incredibly as a composition of stripes.

Textil 3. Digital painting by Myriam B. Mahiques

Brandhorst Museum in Munich, southern Germany. See the composition of stripes makes the painting closer to a fractal design. Photograph: Matthias Schrader/AP

Spalding’s comment about covering the wall has found a response in Germany, in the Brandhorst Museum, Munich. Its painterly facades in geometric stripes of many colors make the building look like a gigantic abstract. Obviously, the Museum is a container for the displays of many contemporary paintings, sculptures and videos. The architecture is an advertisement of what is going on inside. As Jonathan Glancey puts it “This building is the servant of the art inside and not the master, as too many bravura new galleries today can be.” The Museum’s architect, Matthias Sauerbruch explains the façade’s idea was taken from the Neue Pinakothek, the Romanesque art gallery commissioned by the former king Lud Ludwig I of Bavaria in the 1850s. This monumental work, which stood near the Brandhorst, was destroyed by allied bombing during the second world war and has since been replaced by a postmodern building opened in 1981."The outside of Ludwig's building," says Sauerbruch, "was covered in what were effectively huge paintings. You knew it had to be an art gallery. It must have had a magnetic appeal: a building designed to attract a large public and to show them works collected by the Wittelsbach dynasty. We picked up the idea - but, well, inside our museum things are very different."(quoted by J. Glancey). Maybe Sauerbruch was inspired by the propagandistic idea, but I see his resolution goes beyond advertising, while the Neue Pinakothek exhibits the exterior paintings separetely, inside frames of pillasters, the whole Brandhorst Museum is a 3D painting in itself: the Abstract Expressionism has evolved into architecture.

Neue Pinakothek, 1880.reference.findtarget.com/.../Neue%20Pinakothek/

REFERENCES.

Do not adjust your art gallery. In Guardian.co.uk Article by Jonathan Glancey, The Guardian. Thursday 4, June 2009

Julian Spalding. The Eclipse of Art: Tackling the Crisis in Art Today. Prestel, 2003

http://myriammahiques.blogspot.com/search/label/%22Arts%20and%20Architecture%22

Breve Reseña Histórica de Barrios de Inmigrantes Mexicanos en Los Angeles

Primeros inmigrantes granjeros en California. Foto bajada de Internet.

This is an excerpt of my publication in Area No 14, October 2008.

Este texto es parte de mi publicación en Area No 14, Octubre 2008. La versión completa está disponible en Español.

No reproducir sin permiso, por favor solicitar ISBN a mi dirección de email.

La ciudad contemporánea tiene muchas capas de formas construídas superpuestas, lo que es llamado “palimpsesto”; al estudiar la forma urbana corriente de un asentamiento o ciudad, necesitamos buscar razones histórico-sociales y formas primarias de las formas de estructuras morfológicas —que llamaremos “patterns—” que se conforman finalmente.

Muchos autores han relacionado a Los Angeles con modelos fractales. Nuestro objetivo es estudiar un grupo particular de inmigrantes, los mexicanos en el sur de California, y la consecuente forma urbana de esta inmigración.

Desde sus comienzos, Los Angeles fue una ciudad policéntrica, producto de viejos pueblos dispersos. La descentralización en municipalidades fue resultado de la actividad industrial, siendo una de las más importantes la dedicada al petróleo.

Esta ciudad ha sido considerada de puertas abiertas para los inmigrantes de todo el mundo y fundamentalmente para los provenientes de países fronterizos. Pero, el viejo Los Angeles era segregacionista, especialmente en relación a los mexicanos y los residentes méxico-americanos descendientes de aztecas (chicanos).

Los tratados difícilmente detuvieron los problemas raciales que crecieron en 1850, luego de la finalización de la guerra entre México y Estados Unidos. La República Mexicana enfrentó frecuentes invasiones y piraterías que comenzaban en California, por tierra y mar, luego del tratado de Guadalupe Hidalgo (1848). Para 1856 se vislumbraba una guerra civil, como consecuencia de las hostilidades continuas –a modo de guerrillas internas- entre grupos mexicanos en California y autoridades Anglo-americanas. La enemistad se incrementaba, ya que americanos y mexicanos aún vivían en mundos aparte, a pesar del Tratado.

What have been the Mexican American War only a few years earlier became a war against Mexican Americans. The Treaty that ended the U.S. Mexico War had been explicit about the citizenship consequences of peace. Mexicans who stayed would become Americans. (Deverell 2005: 11).

Lo que era una paradoja, los mexicanos no eran americanos, aunque lo fueran por ley. Por ejemplo, Sonoratown, el barrio situado al Norte de la Plaza, no lejos de la rivera del río Los Angeles, estaba ubicado de hecho en Los Angeles, California, es decir en Estados Unidos, pero su identidad, sus costumbres, su realidad social, pertenecían a México, al menos para cualquier anglo angelino.

La guerra civil quedó sin efecto, pero estas fricciones, con diversos matices, continuaron en el siglo XXI en la moderna metrópolis.

Quemando una villa mexicana en Los Angeles, 1924. Foto bajada de Internet

El brote de peste bubónica en 1924 fue atribuído a las extremas condiciones de pobreza de las viviendas de emergencia de inmigrantes. Su demolición y los incendios causados por razones sanitarias condujeron a un cambio radical en la morfología de la ciudad. Los barrios mexicanos más afectados desaparecieron por esta política de tabula rasa que no consideró la reubicación de los pobladores mexicanos.

A lo largo del tiempo, se sucedieron nuevos arribos de mexicanos y Los Angeles ya no pudo rechazar sus raíces culturales mexicanas y sus modelos de apropiación cultural.

La mayor parte de los inmigrantes mexicanos se radicaron en el sudoeste. En 1930, el 30% de los chicanos vivían en California prestando mano de obra barata semi y no especializada para el sistema ferroviario entre ciudades. Dicha inmigración modificó también los modelos residenciales chicanos. Ellos se establecieron en viviendas de construcción precaria, a la merced de las inundaciones en las márgenes del río Los Angeles, y en los viejos vecindarios, ocasionando superpoblación. Las fotografías muestran un modelo urbano caótico sin orden, con excepción de calles incipientes. Los patios solían ser cubiertos con techos provisorios que se superponían a otros techos vecinos. El orden euclidiano solo era verificado en la grilla de calles, y no tan estrictamente, si tenemos en cuenta que las calles siguen la geografía montañosa y en varios lugares se quiebran en diferentes niveles. Dentro de los espacios remanentes, no había orden, en términos euclideanos.

Mapa étnico de Los Angeles en 1950. Imagen bajada de Internet

Los Angeles en 1875. Fotografía bajada de Internet.

A menudo, dos o tres casuchas eran construidas en un lote pequeño, dejando apenas lugar libre. El censo de cuadras en el corazón de la ciudad de 1928 reportaba 317 viviendas conteniendo una población de 1509 personas —un promedio de 40 casas por cuadra y 4.8 personas por casa. La iluminación y ventilación usualmente era pobre y la plomería se hallaba en condiciones subestandard, con un promedio de un baño cada seis u ocho familias.

Para mediados del siglo XX, población blanca —principalmente sureños pobres— se concentró cerca de la zona industrial, en Bellflower, Bell Gardens, Cudahy y Downey, separada por una zona algodonera (Soja 2000: 133), a lo largo de la avenida Alameda, del ghetto negro hasta el Oeste (ubicado primariamente dentro de la ciudad de Los Angeles). Desde entonces, se fueron mudando a los alrededores del condado de Los Angeles y más allá aún, en un claro desplazamiento social, clases más acomodadas de trabajadores blancos.

Así quedaron los chicanos agrupados en y alrededor del barrio Este de Los Angeles. Sin un apoyo impositivo y control estatal, estas áreas quedaron sumidas en la pobreza, la superpoblación, con viviendas y empleos en crisis. El gobierno federal, sin embargo, estaba enfocado en otro lugar: el complejo militar industrial, desde que ocurrió Pearl Harbour hasta las guerras con Corea y Vietnam. La presencia de personal militar estratégico blanco instigó manifestaciones contra los mexicanos inmigrantes y el Este de Los Angeles quedó relegado a ser un barrio segregado.

Las siguientes fotografías aéreas pertenecen a un sector en el Este de Los Angeles. Fueron bajadas de Google Earth, y estimamos que fueron tomadas varios años atrás. La morfología urbana está compuesta por casas regulares, pero, como históricamente se muestra, arregladas en un pattern irregular. Lo más respetado es el espacio libre al frente mientras que los corazones de manzana están cubiertos con construcciones, que son indicación de la presencia de construcciones ilegales para salvar la superpoblación.

Fotografía aérea del Este de Los Angeles, tomada de Google Earth.

Hacia 1967 los gangs negros del Sur de Los Angeles se mudaron a la ciudad de Compton, desplazando a la población blanca. Ellos fueron mayoría hasta finales de 1970 cuando la inmigración mexicana ilegal comenzó a avasallarlos. Para 1990, barrios enteros habían sido transformados formal y socialmente.

Aunque el censo evidencia una creciente población de mexicanos insertados en otras comunidades, la observación diaria muestra que una comunidad es empujada por otra y su tendencia es a permanecer aislada en grupos.

En la actualidad, Los Angeles se ha vuelto una ciudad de ricos y pobres, mientras que la clase media se aleja cada vez más hacia los suburbios y Orange County. La ciudad comenzó la última década con 372.000 unidades de viviendas superpobladas, de las cuales 102.000 están severamente superpobladas y la situación sigue empeorando. Desde 1990 al 2000, la población se incrementó en 300.000 personas y el número de casas ha crecido, para el mismo lapso de tiempo, en 30.600 (Report of the Housing Crisis Task Forced 2000).

Los habitantes chicanos, como sistema dinámico han encontrado un modo de acomodarse tanto en bungalows como en pequeños y angostos sitios.

Diversidad racial en Los Angeles, 2000. Imagen bajada de Internet.

Blurry Frontiers Between Arts and Architecture

Building-sculpture of "La Mona" in Tijuana. by “Derrick”. From his blog http://derrikchinn.blogspot.com/

As we can see in the following definitions, architecture is completely related to Arts. In the history of modern Art, the collage is an approach to architecture. Collage was invented by the Cubists as a means of exploring the differences between representation and reality. It gave the canvas a 3D dimension.

The first sign of this approach was the experimentation with materials and textures in Post-painterly abstraction; the pure painting seemed to be exhausted, and artists who wished to find their way forward were inclined to abandon temporarily the idea of painted canvas as a vehicle for what they wanted to do or say. This resulted in a new attention to sculpture and an increasing number of experiments with mixed media (E. Lucie-Smith, p. 112), where architecture and art shared a blurry frontier.

Artist Joseph Cornell's box: the 3 dimensions of Art. Web download.

There are some different definitions for the term “Architecture”:

The art and science of designing and erecting buildings based on a functional program and employing the technology available at that time. (Arts and construction)

A style and method of design and construction. (Style and methodology)

Orderly arrangement of parts; structure (Composition and techtonics).

The result of all the constituent elements originated in the relationship between the space that a building produces and its surrounding space. (Architecture conforming and transforming space).

Traditionally, architecture has been considered one of the six Beautiful Arts; in the best of its manifestations, Architecture conjoins beauty and utility, to a degree that both interactive characteristics become essential. It is said that it is only Art when the construction is the expression of a society’s spiritual will in a certain period of history.

The Roman architect Marco Vitruvio (SI BC), in his treaty L’Architettura, says that architecture rests in three principles: the beauty (Venustas) the building possesses; the firmness (Firmitas), or supporting structure; the utility (Utilitas) or function to which the building is destined. In SXV, the architect and artist Leon Battista Alberti sustained that architecture was a construction where the movement of the weights and the union of the bodies, was adapted, of the most beautiful form, to the own needs of the human beings. In SXIX, the architect and theorist Eugene Viollet-le-Duc considered that Architecture or the art of build, had two parts equally important: theory and practice; the art critic and social thinker John Ruskin (1849), who was concerned about socio-cultural and economical issues, defined the architecture as the art of decorate and compose buildings of any destiny which contemplation should contribute to health, strength and pleasure of the human spirit. In modern times, the historian Sigfried Giedion stipulated that the architectural creation was the correct application of materials and of the economic principles to the creation of spaces for the man.

Resuming, in theory, while a building complies with conditions of firmness, function and beauty, it will be considered a work of architecture. And Art, by definition, is the quality, production, expression, or realm, according to aesthetic principles, of what is beautiful, appealing, or of more than ordinary significance. If Art means to satisfy human spirits, then, it has no need for “Utilitas”, though it needs Venustas and Firmitas.

In the last fifty years, beginning with pop art, these considerations are not like black and white. In some cases, Art has been eclipsed by non-art and architecture eclipsed by non-architecture. Here, there is no way to find a frontier between both disciplines, both of them are joined in one discipline, maybe I can call it “artchitecture”.

In “artchitecture”, I find four different resolutions –for now-:

1) The bizarre buildings, closer to vernacular architecture, where everything is possible, any shape or alien image that was never related to architecture.

Ladder to access inside "La Mona". The building-sculpture has an access at the back and a window at the breasts location. It is possible to see the neighborhood around once inside the "statue". Picture by “Derrick”. From his blog http://derrikchinn.blogspot.com/

A bizarre house in Baja California, Mexico.http://www.flickr.com/photos/xdisone/3094148962/

2) The buildings as a clear manifestation of a recognizable artistic style. In this category, I would add the appropriate technology constructions that also belong to landscape and natural art.

Coca Cola building in Las Vegas. Once you approach it, it is possible to see the standard interior floor plans. The sculpture consists of a glass liner, with the shape of a Coke bottle. It is a reminder of pop art with a clean technology. From commons.wikimedia.org/wiki/File:Coca_Cola_bui...

3) Buildings where one or two of the three Vitruvian standard principles are missing, in consequence, the building could be considered a work of art, though it also contains the function….

House in Poland challenging "Firmitas". Created by Polish businessman and philanthropist, Daniel Czapiewski.The house represents the Communist era and the state of the world.http://quazen.com/arts/architecture/crazy-and-bizarre-architecture/

Cantilevered house. This one defies gravity. Cantilever houses use a beam supporting on only one end. The beam carries the entire load of the building without any other external help. Though "Firmitas" is correct, our perception of lack of gravity makes it appear as an object of art. http://quazen.com/arts/architecture/crazy-and-bizarre-architecture/

4) Buildings where the materiality is not conventional and is closer to the collages or installations ideas. The structure (Firmitas) cannot be seen as typical as it is a consequence of utilizing innovative materials due to lack of the standard ones. It is close to vernacular architecture.

Glass bottle house. From Weburbanist.com

More definitions of architecture will be written in SXXI, as there are new dimensions involved. As the scientific dimension, the one that Vitruvio never dreamt of. Genetic manipulation applied to construction materials, virtual spaces, robots building perfect digital designs in the middle of the New York streets, designs that do not contain the imperfections of human labor. So impeccable they are, that any artistic form is developed, for any function and material: "We marry the digital reality of the computer with the material reality of a building," (Science Daily.com, 2009) say the two architects in charge of my NY’s example, Fabio Gramazio and Matthias Kohler, who both teach and research at ETH Zurich. They call this approach "digital materiality", term that is not found in any of the historical treaties.

REFERENCES

http://www.almendron.com/arte/arquitectura/claves_arquitectura/ca_01/ca_011/arquitectura_011.htm
http://www.myetymology.com/encyclopedia/Architecture.html
Robot Builds Brick Wall In New York City. In Science News. October 26, 2009
http://www.sciencedaily.com/releases/2009/10/091026133016.htm
Lucie-Smith Edward. Movements in art since 1945. Singapore, 1995.

The City in Physical Layers

Sierpinsky fractal en 3D, by Johnny Layne. From www.graynod.org/johnny/screenshots.html

The fractal dimension of cities in 2D will be always a value between zero and two. If we calculate the fractal dimension of Buenos Aires, we will see that its value does not differ - at least significantly - of the values reached in other cities. For example, at the neighborhood scale, La Boca (Buenos Aires) is in the range of D=1.80, the same is for East Los Angeles in California. Considering that they are two very different cities, this reduccionist analysis would not be enough to understand the morphological patterns of the city.

One of the important aspects is the constitution of the city in layers. And this time I do not refer to socio-cultural questions, but material constructions in layers.

In this regard, I recall a comment from the architect-archaeologist Dr. Daniel Schavelzon, who, on the Mayan cities, said "........ of NONE historical (excavated) city we have the real floor plan, it is not even possible with the techniques and methods of archeology itself, to have a floor plan of a particular moment in time ....... But our culture works on destruction-construction, which never existed before, it was physical overlay architectures. One above the other, with the abandonment, the contemporary stages between each building were destroyed. Yes, it is complex ,........."

What is the objective to reach in our spatial scale of analysis? Isn't it that cities exist in layers like Jericho and Troya, a city, superimposed to other, and other.....? In the comparison of cities, this issue will be of supreme importance.

Returning to the case of Buenos Aires-Los Angeles, the second, for being located in a seismic region, lack the multiple undergrounds and mysterious tunnels of Downtown Buenos Aires. This outline is to understand that the question does not finish here.

Buenos Aires also has aerial cables and signs that make very different the pedestrian's perception. Los Angeles appears like a city visually ¨cleaner¨. Therefore, depending on the scale selected, these visual elements should be kept in mind.

Two different layers, both graphics are ready for the fractal D calculation. By M. Mahiques

Visualization in 3D of the concepts discussed here. Picture: Internet download.

There is a methodology, for the physicists, and it is the analysis by means of ¨fractal cheeses¨, called this way because of their complex three-dimensional morphology, similar to gruyere cheeses of fractal dimension D between 2 and 3, being 3 the value of the solid cube. These graphs bear extremely complex and unreachable formulas for architects. It is for this reason that I propose humble fractal and lacunarities mensurations in 2D, but in different levels. And the comparative analysis will be simpler, we can draw graphics in 3D but these will be the expression of the results of the layers. Should we wonder then, do we study buildings or a summation of buildings in the space-time? in which period do we produce the temporary cut to carry out the analysis, if everything is constantly transforming? Do we have to be satisfied with contemplation and reach conclusions from the mere observation?

La Ciudad en Capas Físicas

Carpeta de Sierpinsky en 3D, por Johnny Layne. Bajada de www.graynod.org/johnny/screenshots.html

La medición fractal de ciudades en 2D siempre será un valor entre 0 y dos. Si tomamos la medición fractal de Buenos Aires, veremos que su valor no difiere –al menos significativamente- de los valores alcanzados en otras ciudades. Por ejemplo, en la escala barrial, La Boca (Buenos Aires) está en el rango de 1.80, lo mismo que el Este de Los Angeles en California. Considerando que son dos ciudades muy distintas, este análisis reduccionista no sería suficiente para comprender las características morfológicas de la ciudad.

Uno de los aspectos importantes es la constitución de la ciudad en capas. Y esta vez no me refiero a cuestiones socio-culturales, sino construcciones materiales en capas.

Al respecto, recuerdo un comentario del arquitecto-arqueólogo Dr. Daniel Schavelzon, quien al respecto de las ciudades mayas, me decía “........de NINGUNA ciudad histórica (excavada) tenemos su planta real; ni siquiera es posible por las técnicas y métodos de la arqueología misma, tener una planta de un momento determinado en el tiempo....... Pero nuestra cultura funciona por destrucción-construcción, cosa que nunca existió antes, se hacía superposición física de arquitecturas. Una encima de otra; con el abandono se destruyeron las diferentes etapas no contemporáneas entre uno y otro edificio. Sí, es complejo,.........”

Hasta dónde hemos de llegar en nuestra escala espacial de análisis? Acaso no existen ciudades en layers como Jerico y Troya, una ciudad, sobre otra, sobre otra.....? En la comparación de ciudades, este ítem será de suma importancia.

Volviendo al caso de Buenos Aires-Los Angeles, la segunda por estar en una región sísmica, carece de los múltiples subsuelos y misteriosos túneles del Centro de Buenos Aires. Este esquema es para comprender que la cuestión no termina ahí.

Buenos Aires cuenta además con cables aéreos y carteles que hacen muy distinta la percepción del transeúnte. Los Angeles aparece como una ciudad visualmente ¨más limpia¨. Por lo tanto, dependiendo de la escala de trabajo, incluso estos elementos visuales debieran tenerse en cuenta.

Hay una metodología, para los físicos, y es el análisis por medio de ¨quesos fractales¨, llamados así por su compleja morfología tridimensional que asemeja a quesos gruyere de dimensión fractal D entre 2 y 3, siendo 3 el valor del cubo sólido. Estas gráficas conllevan fórmulas sumamente complejas e inalcanzables para arquitectos. Es por ello que propongo humildes mediciones fractales y de lacunarios en 2D, pero en distintos niveles. Y el análisis comparativo será más sencillo, podemos dibujar gráficas en 3D pero éstas serán la expresión de los resultados de las capas. Debiéramos preguntarnos entonces, estudiamos edificios o una sumatoria de edificios en el espacio-tiempo? En qué momento producimos el corte temporal para realizar el análisis, si todo se transforma constantemente? ¿Hemos de contentarnos con observar y sacar conclusiones de la mera observación?

Population and Dissipative Dynamical Systems

Airplane vortex. courses.gnowledge.org/lessonsview?ssid=3394

Dissipative systems are those that use the energy to maintain their form, as the atmospheric vortexes or alive organisms. If we consider for ex., a pendulum, under ideal conditions it would not stop, but under normal conditions, it would arrive to its point of minimum energy to continue moving and then it would stop. Now, if we take a multidirectional system of pendulums, small interferences could cause an avalanche in the system. These interferences can grow and spread through the system with very little resistance. As the energy vanishes in this process, this should be fed so that the avalanches continue.

Landslide induced by an earthquake over a neighborhood near Santal Tecla, El Salvador. 2001.http://carletong.files.wordpress.com/2009/04/landslide1.jpg

Another simple example would be that of the pile of sand. If we slowly add sand to a pile full with sand, a re-accommodation of particles will only take place. The individual grains of sand (or grades of freedom) will not interact in big distances. Continuing the process, we will end up increasing the pile achieving a critical value, with a slope that will produce an avalanche. The pile cannot already be described by means of local degrees of freedom. The distribution of avalanches follows a law of power.

The dissipative systems act opposing to the intent of displacing them of the state where they are. That is to say, they contain regulatory properties. In the dissipation, in the irreversibility, in the lost of equilibrium, is the key of evolution.

Mechanically speaking, dissipative systems are dynamical systems that are characterized by an “internal friction” that tends to contract phase space volume elements. Phase space is a mathematical space spanned by the dependent variables of the dynamical system. In our example of the pendulum, it has a one-dimension movement with a two-dimensional phase space spanned by the position and momentum variables.

These theoretical aspects are not exclusive of the physics, they are also applicable in urban morphology to population's limitless growth, to the ¨urban sprawl¨, and its search of organization levels; to cities and buildings’ overcrowding; to conventillos generation; to the multiple illegal constructions; “hot beds” (camas calientes) habits, usually the result of continuous arrival of immigrants. Severe analogical cases are the refugees coming massively to a country, local habitants being the original “pile of sand”. The system will reach a critical point where the internal regulatory properties will intend to look for the equilibrium. These properties may be reflected in the law, the “razzias”, the deportations, or the provision of dwellings and jobs opportunities, among other situations.

Refugees from Rwanda arrive in Tanzania. Photo by UNHCR/ P. Moumtzis. http://nocameranointervention.files.wordpress.com/2009/03/refugees9.jpg

The energy models provide us helpful analytic tools that explain the development of the societies, their collapse, the wars, the religions. It is considered that the human communities are dissipative systems, because they are in constant fluctuation, and life is in itself an expansible process.

Further readings (for glossary)
http://www.cna.org/isaac/Glossb.htm#Dissipative

Morfología Urbana de Buenos Aires y Geometría Fractal

Analogy between a block in La Boca neighborhood and the Sierpinski gasket.

Analogía entre una manzana de La Boca y la carpeta de Sierpinski. Personal archives.

The following is an excerpt of my article for the proceedings at SEMA Morphology Symposium.

El siguiente texto es parte de mi artículo para el Congreso de Morfología SEMA, 2003.

No reproducir el texto sin permiso.

“De hecho geometría y orden son en más de un caso sinónimos. Para ello basta pensar que así como hay geometrías en plural, con sentidos dialécticos, complementarios y/o antagónicos... también hay niveles de orden en plural y nadie puede fijar frontera exacta entre orden y desorden. Una sociedad humana en tanto grupo constituido sobre la base de un orden de sus interrelaciones implica una geometría de hombres”. (G. Breyer, 2000)

La forma es relativa a nuestro acto de registro de la misma. Hay muchos diseños que son estrictamente euclidianos, pero puede suceder que terminen en versiones fractalizadas, un ejemplo interesante es el quincunx que representa la “luz de Alá”, en las culturas africana y afro-americana. Este símbolo religioso parte de cinco cuadrados, con uno en el centro y uno en cada esquina, finalmente, luego de varias iteraciones, el patrón geométrico es recursivo, por lo tanto es un fractal. Y a veces, el fractal está encubierto, se descubrirá en el cambio de escala, por ejemplo, una aspirina de forma cilíndrica se ve como un hermoso fractal multicolor bajo el microscopio.

Un ejemplo de fractal no intencional, puede encontrarse en los procesos de dinámicas sociales de crecimiento urbano –inconsciente-, que denotan bordes sumamente irregulares. A este tipo de fractal se lo clasifica como DLA (“difussion limited aggregation”), debido a su analogía con el comportamiento de partículas en una solución, atraídas por un electrodo.

En escalas más pequeñas, podríamos suponer, que las ciudades planificadas, -donde el sujeto impone su geometría sobre el medio-, son típicamente euclidianas, pero esta postura se desmorona cuando cambiamos nuevamente la escala y comenzamos a estudiar el tejido de las manzanas típicas de Buenos Aires. Análogamente al quincux, las figuras euclidianas se entremezclan en una urdimbre hasta conformar un fractal, que será plausible de análisis por sus bordes o sus superficies, en plural, ya que cada sección del mismo mostrará distintas conformaciones que resultarán en diferentes valores de dimensión fractal.

-Un fractal tiene una estructura fina; esto es, detalle en escalas arbitrariamente pequeñas, y tiene la propiedad de auto-semejanza, quizás aproximada o estadística. También se caracterizan por su propiedad de ser invariantes ante cambios de escala, aún en la más pequeña.-

El ejemplo de las distintas iteraciones de la Carpeta de Sierpinski hace evidente que las propiedades fractales se refieren a la organización espacial de un patrón, a través de distintas escalas –niveles- de observación: satelital, regional, áreas metropolitanas, pueblos, secciones de pueblos y ciudades, manzanas o conglomerados. Estos patterns pueden consistir en subconjuntos con diferente dimensión fractal, que muestran un comportamiento multifractal.  Pero si un fractal tiene una estructura fina, también deberíamos verificar qué sucede cuando continuamos nuestra observación para escalas menores. Amos Rapoport sostiene, por ejemplo, que la arquitectura doméstica muestra claramente su carácter compositivo: “edificios dentro de edificios”, el techo de una vivienda puede tener una evolución independiente relativa, incluso considera al fuego –ya incorporando significados simbólicos- como un tipo primordial de “edificio” de evolución independiente aunque integrado a la casa; también podemos llegar a la escala del material componente y su textura, etc. Cada forma, sin embargo, no es vista como una entidad aislada sino en función de sus antecedentes: los caracteres de individuación se relacionan a los de la entidad mayor.

“A primera vista nada parece semejar menos a Eudoxia que el dibujo del tapiz, ordenado en figuras simétricas que repiten sus motivos a lo largo de líneas rectas y circulares, entretejido de hebras de colores esplendorosos, cuyas tramas alternadas puedes seguir a lo largo de toda la urdimbre. Pero si te detienes a observarlo con atención, te convences de que a cada lugar del tapiz corresponden un lugar de la ciudad y que todas las cosas contenidas en la ciudad están comprendidas en el dibujo, dispuestas según sus verdaderas relaciones que escapan a tu ojo distraído por el trajín.....”(de “Las Ciudades Invisibles”, Italo Calvino)

Pareciera ser que la búsqueda del conocimiento es perpetua, y ya en una concepción más abarcadora, en niveles metafísicos, difícilmente podamos separar la comprensión de la forma de las sensaciones y los efectos físicos; incursionar el diseño en el espacio gravitacional implica ya un conocimiento de tales efectos, incursionar en el espacio subterráneo también, tal vez sea lo que llevó a algunos vanguardistas a buscar los sonidos de la descomposición subterráneos de las tumbas de personajes famosos –como Borges-, en una curiosa forma de “arte”?

“El estudio de la espacialidad es clave en la producción del conocimiento, en la auto-referencialidad del ser humano, en la construcción del sujeto” (Doberti, 2003).

The Chaos Game: Some Considerations About Urban Patterns

The Chaos game. IFS Fern structure generated by Myriam Mahiques. See the difference for both iterations.

Michael Fielding Barnsley is a researcher mathematician who has worked on fractal compression. By the time Mandelbrot had resolved his set, Barnsley was taking a different road. He was thinking about nature’s images and patterns generated by living organisms. He experimented with Julia sets, always trying to achieve greater variables. Until he realized that randomness was the basis for modeling natural shapes. He used the term “chaos game” to refer the global construction of fractals by means of iterated function systems.

Julia sets, that are outcomes of deterministic processes, proved to have a second valid existence as the limit of a random process. Barnsley suggested an analogy for this situation: one could imagine a map of Great Britain drawn in chalk on the floor of a room. A surveyor could find it complicated to measure this awkward shape with fractal coastlines. But, if grains of rice are thrown into the air, allowing them to fall randomly on the floor, these grains inside the map could be counted. As times goes on, the result begins to approach the area of the map. That is the limit of the random process.

Barnsley and his co-workers produced images of nature by writing down a set of simple rules randomly iterated; the question was how to reverse the process: given a particular shape, how to choose a set of rules. The answer, which he called a “collage theorem” was pretty simple. One can begin drawing the shape to be reproduced. Then, using a computer terminal and a mouse as a pointing device, small copies of this shape would be overlaid on the original image, not exactly on top of it, if needed. A highly fractal shape could easily be tiled with copies of itself and at some level of fractal approximation, every shape could be tiled. However, in Barnsley’s technique, the chances serve as a tool, because the results are deterministic and predictable.

To generate a fern leaf with the chaos game, each new point falls randomly, but gradually the fern emerges.

I take this theory as a reflection for urban patterns. To define a shape, Barnsley had two ways, working in superimposed layers or using falling random points. Applying the concept to urban morphologies, if we use a fractal as an analogical model, we need to understand if the fractal generation is consistent with the urban fabric generation. If not, the fractal will be just a simple drawing in 2D with a similar shape. Nothing else. A fishbone structure, is an abstract simplification of the fern pattern. An analogy for the city, would be an axis (an avenue) and lateral oblique streets. But if the city was planned and not generated by random aggregated houses, Barnsley fern is not a good comparison. Or, we can consider the superimposed layers and find out if it works.

This example of an aerial picture of a neighborhood in China, shows us the different criterion on the subject. Though the regional scale is arranged with cross streets –not exactly a quadrille- the houses are located in straight lines perpendicular to main axes. The first approximation to urban morphology analysis is the Euclidean pattern of lines (houses alignment) across an axis.

Houses alignment. Personal archives.

A fractal pattern discovered through filters. Personal archives.

All patterns together in overlaid layers. Personal archives.

If I decide to work on the image, and see what is behind those lines, I sharpen the edges, make it binary and now I have a fractal pattern with the streets already there, it is not Euclidean any more, as the urban fabric is emphasized over the streets. And if I keep on working, I can see the possibilities of overlapping layers, as Barnsley’s example. That is a more complex fractal image that contains all the information of streets and urban fabric. Compared to Barnsley’s pictures of nature I would say this is a “superfractal”. All three concepts are correct, the difference is which aspect of the urban form will be studied to accomplish our objectives. It is only a matter of professional experience to choose the best one.

REFERENCES

Gleick, James. Chaos. Making a new science. USA. 1987

Barnsley web site:

http://www.superfractals.com/default.htm