REFERENCE: "STUCTURE OF CITIES INSIDE CITIES: Morphlogical analysis of Chan Chan" MYRIAM B. MAHIQUES
JOURNAL OF MATHEMATICS & DESIGN, PP. 61-77, VOLUME 11, NUMBER 1, 2011, ISSN 1515-7881.
Resumen
Mucho
se ha avanzado en las posibles representaciones de una ciudad, y los cambios
más significativos han surgido en la abstracción de imágenes que representan
los complejos fenómenos urbanos en pos de una lectura más sencilla: el
desarrollo de Google Earth de acceso público y gratuito, imágenes satelitales
actuales, imágenes digitales en general. Todo el acceso a información que se
nos permite, sumado a las múltiples herramientas digitales, hace que nos
replanteemos cuál es la mejor forma visual de analizar la ciudad.
La aplicación de la geometría fractal en
modelización espacial responde a un
método para analizar formas, que permite la comparación entre modelos espaciales y estructuras empíricas.
La metodología consiste en interpretar estas estructuras empíricas (ciudades,
barrios, asentamientos, fachadas, etc) como fractales aleatorios o
estocásticos. La geometría no es medición en sí misma, pero es interactiva
entre la modelización y la medición.
La medición
consiste en dar valores a los fenómenos que nos interesan, dentro de un marco
establecido.
A los
efectos de ilustrar estos conceptos, analizaremos las primitivas ciudadelas de
Chan Chan, en Trujillo, Perú (aprox. Año 1000 D.C.), que tienen la particularidad
de estructurarse como ciudades dentro de otras ciudades. Nos basaremos en el
trabajo de campo y publicaciones de eminentes arqueólogos y antropólogos para
todos los aspectos descriptivos, y a continuación, demostraremos que, a pesar
de las concepciones generalizadas de clasificar el medioambiente construido
prehistórico en la mera construcción y la arquitectura en intención artística,
el modelo morfológico urbano de la cultura Chimu es la expresión geométrica de los espacios cognitivos
resultados de su experiencia como miembros de un grupo social. Veremos que en
lo que desde la vista aérea se percibe como una forma de cuadrículas
Euclidianas combinadas entre sí, existe un patrón morfológico no evidente de
características cuasi literales de fractalidad, que otorgan una gran riqueza
espacial. El tema es más sorprendente aún si consideramos que estos diseños
urbanos son intuitivos y representan una gran evolución con respecto a las
antiguas configuraciones urbanas de ejes ceremoniales.
Abstract
A lot has been advanced in the possible
representations of a city, and the most significant changes have arisen in the
abstraction of images that represent the complex urban phenomena for a simpler
reading: the development of Google Earth of public and free access, updated
satellite images, digital images in general. The whole access to information
that we are allowed, added to the multiple digital tools, makes that we
reconsider which one is the best visual form of analyzing the city .
The application of the fractal geometry in space
modelization responds to a method to analyze forms that allows the comparison
between space models and empiric structures. The methodology consists on
interpreting these empiric structures (cities, neighborhoods, settlements, facades,
etc) as random or stochastic fractals. The geometry is not measurement in
itself, but it is interactive between the modelization and measurements.
The Dimension consists on giving values to the
phenomena that interest us, inside an established boundary.
To illustrate these concepts, we will take the
primitive citadels of Chan Chan, in Trujillo, Peru (approx. Year 1000 D.C.)
that have the particularity of being structured as cities inside other cities.
We will be based on the field work of eminent archaeologists' and
anthropologists´ publications for all the descriptive aspects, and next, we
will demonstrate that, in spite of the widespread conceptions of classifying
the prehistoric built environment in the mere construction and the architecture
in artistic intention, the urban morphological pattern of the culture Chimu is
the geometric expression of the cognitive spaces of its experience like members
of a social group. We will see that in what is perceived from the air view like
a form of Euclidian grids combined to each other, a non evident morphological
pattern exists of quasi literal characteristics of fractality that grant a
great space richness. The topic is even more surprising if we consider that
these urban designs are intuitive and they represent a great evolution with
regard to the old urban configurations of ceremonial axes.
DESCRIPTION OF THE CITADELS IN RELATION TO
INHABITING PRACTICES
The Chimú Empire (950-1440 AD) extended along the
Peruvian coast from Tumbez in the North to Lima in the South. Chan Chan,
located in the Moche valley, was the capital of the Empire centralizing all the
services. Built in adobe, was the biggest pre-Columbian urban center in South
America, currently declared UNESCO World Heritage, since 1986.
The citadels are big settlements that contain a
great number of monumental buildings. Six of them were named in honor of
explorers and archaeologists that worked in the place: Squier, Bandelier,
Rubber, Tschudi, Rivero, Velarde, and Tello. The other citadels are denominated
Great Chimú, Chaihuac and Laberinto
. The small structures are
the Huacas
.
The civic constructions served to the aristocracy
and the State, while the proletariat consisting in artisans, personal of
service and farmers lived in dispersed neighborhoods outside of these
monumental centers. The palaces articulated the urban space, since each king
built his government place during his life and then this became monument after
his death.
Michael E. Moseley and Carol J. Mackey (1973, 1974),
after their investigations in 1967 and 1969, formulated the hypothesis that
once the Curaca (ruler) died and buried in the ¨funerary platform¨, all its
citadel was transformed into an enormous catafalque where his servants, women,
court characters and priests, were sacrificed and buried to accompany him and
to serve him in “the other life”. In turn, the following ruler ordered to build
his own palace citadel. Presumed habit, very similar to those of their
successors, the Inca.
In synthesis, Chan Chan
shows three urban typologies:
1)
The slums, of agglutinated
rooms, without surrounding walls, dispersed without apparent order in the
Western suburbs. More complex than simple cabins and associated to cemeteries
of adobe chambers with double walls.
2)
An intermediate tipology
located among the citadels, without a specific planning, represented by
enclosures with niches, of regular geometries, also with lower surrounding
walls and other similar attributes to those of the monumental architecture, but
of smaller scale. The biggest ones show a more rigorous planning of patios,
passages and storage rooms, in comparison with the smallest of more domestic
characteristics. Seemingly the use was
residence of social classes
3)
The royal architecture of the
citadels, of monumental character that, obviously did not reflect population's
density, since many works were carried out by
non resident workers.
Each citadel was surrounded of adobe walls of
approximately ten meters high covered
with a soft mortar in which intricate designs of birds were carved, mamals,
fish, in two styles, one more realistic and the other one more stylized and
abstract.
An interesting aspect is that there are not openings to
the North, although these are the walls more exhibited to the sun in detriment
of the fog; the highest walls protect against the winds of the SO coast. The
combination of these walls configurate a labyrinth, and, in turn, each
inhabitable structure has multiple internal walls that form an intricate space
of corridors, rooms, covered with the elite's artistic expressions.
Great part of the constructions is due to these beliefs. The sacrifices and
other methods of ritual violence were imbued in the Andean cultural practices.
The cosmological principles, the phenomena, the religion
and the social order were connected to the exercise of the power, and it was
still maintained after the death of the Curaca who was confined in his palace
so that the vassals could not perceive
his mortality. The lack of respect to the temples, the disobedience to the law
was severely punished burying the culprit alive.
This concept where the physical and the social world correspond each other,
is denominated doxa, term used by the
sociologist Pierre Bourdieu in humanist instances that implies the limitation
of the social mobility inside the social space; the imposition of limits for
each individual like symbolic force of the political power. Some cultural
objects are recognized as doxa to be inappropriate for a certain social
position. Doxa contains the sense of "one's place", and the sense of
ownership. The sacred landscape is also a symbolic way to establish social
orders.
F1.
Partial view of a citadel
F2. Niches
F3.
Altar
F4.
Decorated walls with the pattern of fishing nets
METHODOLOGY OF URBAN MORPHOLOGY
ANALYSIS
Our first step consists on verifying if the citadels,
taken on the whole, present fractal characteristics. We will use the method Box
Counting to find the fractal dimension (D), the software is
Fractalyse.
For the complexity of the pictures, we will apply the
filter ¨sharpen¨ to get more contrast. Then, the file. jpg is converted into
binary to carry out the mensuration.
It also interests
us to verify if, given a condition of fractality, it is also verified when we
select sectors of the citadels. That is to say, if a part of the whole can be
representative of the complete morphological urban structure. We will analyze
the whole and three sectors of the same one. Of the main characteristics of a
fractal, we will focus on the autosimilarity. Fractals define a complex
hierarchical scale in each level, where the deterministic fractals show the
same structure in each magnification. When the exact autosimilarity is lost,
and some structural properties are only similar in each scale, we are before
fractals of statistical autosimilarity more representative of the conditions of
the real life, and they still continue presenting hierarchical connections of
texture and/or shape in the different scale levels.
The concept of
similarity explores a certain phenomenon, its immediate environment and its
relationships with other phenomena. Generally, two phenomena are similar when
they share attributes and circumstances. The similarity is governed by the
context (function, users, reasons...), scale, techniques of recognition and
mensuration. The grade of similarity is a resultant between a model and an
objective; and not only of their attributes but also of their relationships. In
our investigation field, the objective goes from pixels, to regions, in a
context and a scale that we will define. From a perspective of the informatics,
similarity can be described like a system that
allows the data to be comparable
under the criteria that the user specifies as similarity.
There are different
forms to approach to the concept of similarity.
For example, an
efficient study of objects that share a
similar form.
Or that share similar
areas.
Or that derive in
possible transmutations, like forms of analogical inference.
Explicit or implicit
similarities exist according to the context.
The simplest way of
images evaluation is to compare its
visualities, as measure, shape, color,
texture and other components that we can elucidate, either in its entirety or
its segmentations in studies of fractal plot lanes.
The autosimilarity in
urban morphology is interpreted as a design process - fractal property - and it
is appropriate to the clinical interpretations of images, where a collection of
interpretations of the sub-parts is part of a whole. Then, it is verified if
this whole is similar to another image's whole and equally, as these sub-parts
of the other whole is similar to those of the original pattern.
The resolution in scales
can affect the comparisons, because
different morphological structures could appear in the scaling variations. We can apply the theories of fractal hierarchies
but, sometimes, the environmental and habitat issues are superimposed and we do not always find
scaling autosimilarity. But yes we can find the tendencies.
F5. The group of citadels. The slums are located on the West side, in our
figure, along and to the left.
F6. Sector 1
F7. Sector 2
F8. Sector 3
Table 1. Table of results with Box Counting method
In the following
figures, we analyze the audiences in the context of the dominant architecture.
Notice that the texture denotes the
irregularities of the desert landscape and some constructions that are not
completely excavated.
F9. Sector of
Ciudadela
F10. Sector of
Ciudadela
F11. Sector of Audiencia
F12. Sector of Audiencia with storages
Table 2. Results with Box Counting method
For both groups of mensurations, we verify that: there
exist a tendency to fractality and autosimilarity through the different urban
scales, which a Fractal Dimension (D) fluctuating between 1.70 and 1.75.
What still makes the
theory even more interesting, is
the progression in complexity in the U structure as time goes by, of the
audiences to the variants of audiences combined with trocaderos that in
turn, are related to the three major
type of adobe brick proposed by Alan Kolata (1982). That is:
1) high, which dimension
in height is bigger to that of the width.
2) cubic, with similar
dimensions on high, wide and depth.
3) wide, more similar to
our contemporary brick.
The formal evolution becomes from a simple U structure
with a chamber to the typical insert of six chambers, that is a geometric
recursivity of fractal type that is more complex as these cells of six chambers
become primary and they take their own recursivity. The example of figure 13 is one of the so many variations in
the evolution in the U structures. In general terms we are before designs that
share the same pattern of cells, (read it as structure, model) that seen as a
group, look like squares inside squares. From our point of
view, it is also very suggestive the
disposition of the carvings of dragons in Huaca of the Dragón, where the
dragons with their fires contain Moche snakes
of two heads. We have counted a
succession (or conceptual iteration?) of three in a wall partition.
F13. Conceptual iteration of the U structure
F14. Formal articulation between two U structures
The concept of boxes inside boxes has taken us to compare
the mensurations of D with the Sierpinski carpet. Nevertheless, this is more
compact, with a fractal dimension of approximately 1.8928 against 1.75 of Chan
Chan. Logical results if one keeps in mind the quantity of patios and chambers.
F15.
Sierpinski Carpet
A more precise methodology consists on looking for a
second underlying structure, subjected to a primary one that is visible to the expert
eye. So, we intend to verify the Fourier transform applied to one of the
audiences. The software utilized is Fractalyse.
F16. Fourier Transform applied to an Audiencia
The spectrum of gray
is uniform and a structure arises in diagonal, with other approximately
parallel lines that, understood from our previous experience with applications
of Fourier for blocks in the neighborhood of La Boca (Buenos Aires), we
conclude that there is another pattern of space covering, different to that of
boxes and more appropriate to that of curves filling the plane.
The articulation in the U structures takes us to the consideration that these
representative urban forms of the Chimú royalty, go covering the plane with a
similar development to those of the Peano curves. The Peano fractal ¨comienza con
un segmento unitario que se divide en tres partes iguales y el camino recorrido
incluye nueve segmentos, cada uno de los cuales tiene una longitud de 1/3¨. (V.
Spinadel, J. G y J. H. Perera. Geometría Fractal, p. 23, 2007).
(¨it begins with a single segment that is divided in
three equal parts and the path includes nine segments, each of which has a
length of 1/3¨) (My translation)
For the following recursivity level, the fractal dimension is D:1.7491, extremely similar
value to the one taken in the overall urban analysis of Chan Chan and that of
its sectors. What
demonstrates a tendency to the autosimilarity, characteristic property of
fractals, very close to that of the selected analogous fractal.
F17.
Peano fractal
Table 3.
Aplication of the Box Counting method in the Peano fractal
The interpretation about iterations of the curves of
Peano is ours, and applicable to uniform structures of Audiencias. This constitutes an advance
with regard to Kevin Lynch's opinion who defines the citadels like ¨boxes
inside boxes¨, for the used resource of patios and chambers. (K. Lynch, p. 15,
1994). It is very important to point out that this disposition of ¨boxes¨ is
reinforced by the absence of streets and directional axes. However, the
movement and accesses were not irrestrictive, the movements were structured in
independent routes, so much in Chan Chan as in the provincial centers. (Moore,
p.219)
This standardization in
the shape does not seem to be random, but rather it has been a consequence of an important economic change,
of the society progress, based on a basic agrarian economy to an economy of
crafts type goods of production. The complex system required of a bigger
economic control that manifested in efficient standard forms, in other words, a
functionality based on a common system
of interpretation for different administrators, like a rudimentary computerized database of the epoch. The paradox, is that
the higher standardization in the shape,
the more complex the resultant morphological pattern of the possible
compositions becomes, until supporting a fractal structure of astonishing analogy
with those digitally created.
It is also important the
relationship with similar structures in the rural neighborhood; it implies an
absolute concentration of control and power in the agriculture resources and
irrigation. If the U structures were
specifically for control and storage of goods,
is a theory discussed by John Topic (2003) since he sees this system
like process of flow and saving of information, in a way similar to the quipu , where the architectural elements
reflect the transmission processes from an official to another. For example,
beans, stones could have been stored in recipients and/or bags inside the
containers and niches, to keep non written
quantitative information, but as a mnemonic rule, based on the
memorization of facts represented in an object.
FORM AND SCALE
At plane level the U structures show an uniform hierarchy
and we have already seen that they follow laws of similar intuitive design to
the curves of Peano. However, analyzing in detail, the spatial architectural
resolutions, added to the ritualized practice of the burials under the zero
level are indications that some of these structures have a higher status,
specifically the U structures that
belong to the royal enclosures, while the rest denotes solely administrative
purposes. (J.
Piekarski, 2007).
Andrews (1974) proposes a constructive classification
that we should call scaling hierarchy but not spatial because the height do not
always grow linearly as complexity does. This concept of scaling supports our thesis of tendency to fractality
in its high concept of recursivity. From smaller to bigger, we summarize:
.- The auxilios, linear structures of low walls without
niches, but with carvings.
.- The trocaderos, of smaller span whose name makes
allusion to the Spanish word ¨troca¨ or spaces that go through. Also with their formal variants. With three
or four niches.
.- The arcones, small constructions of low niches that,
as the word indicates are like bins.
.- Audiencias and their variants in U and C shape.
To each one of these classifications it corresponds a
cross section that becomes more complex as the structure increases in size. In
the following figure, we schematically show the corresponding cross sections
(up to down) of: auxilios, trocaderos, arcones and audiencias. Although the
sketches are not in scale, our intention is to point out the relationship among
the U structures, the quantity of niches, the height and excavations for
burials, that could be seen in the trocadero. We could infer that to our first
relationship of size of the structure and complexity of the cross section, it
corresponds a graph of linear growth. But to this idea, the funerals
incorporation is opposed. Let us see it this way : the second graph should
exclude the funeral, because the excavation is full with gravel, earth.
However, conceptually the Chimu culture
has had the intention of working the earth in niches, excavations, mounds, not
only in the urban constructions but also in the landscape and to the purpose of cultivations. A clear example is the sunken
gardens, called puquios. From our point of view, all intentional work on and
underground should be considered in the morphological analysis, independently
of the fillers that take place afterwards.
Making an abstraction of the cross sections, we will see
that from the simple line that indicates a wall, we would pass to another
broken line that implies the wall with carvings (auxilios), plus the successive
similar iterations to the first stadiums of the curve of Minkowski that include
niches and funerals.
F. 18. Schematic
floor plans and cross sections of typical structures. Drawing made by the
author based on the ones published by Andrews.
F. 19. Example of
the first iterations of the Minkowski curve
CONCLUSIONS
The form of an urban
settlement is the result of how its creator glimpses its use, and the social
frame sustains its sense.
The urban morphology of
the citadels of Chan Chan has been born of abstract geometries product of deliberate actions of the human
logical-political thought, with a concrete purpose: the one of being adjusted
to the growing productivity, social separation and control of both, production
and society.
And what the
archaeologists and anthropologists wisely point out is a geometric evolution that neither is
accidental nor it arises of the application of an intentional mathematical
model. We will fix the concept in the following quotation of R.
Doberti:
¨La
transformación, la seriación, la mutación, no son accidentes que les acontezcan
a las formas, más bien parece que su ley es la inestabilidad, la metamorfosis.
Uno de los grandes aportes de la geometría al mundo de las formas es haber
establecido muchas de las leyes de la transformación. Y entonces la geometría
se convierte en una de las destrezas para la construcción y el manejo de la
forma¨. (Roberto Doberti, 2º Jornadas Internacionales de
Mathematics & Design, Special Edition, Vol. 5, No 2. p.61,2005)
¨The transformation, the
seriation, the mutation, are not accidents that happen to shapes, but it seems
that their law is the instability, the metamorphosis. One of the great
contributions of the geometry to the world of the shapes is having established
many of the transformation laws. An then, the geometry is converted into one of
the achievements for the construction and the management of shape¨. (My
translation).
We have seen that the
citadels possess a certain autosimilarity whose approximate value of D is 1.75
and its morphological structure contains two basic concepts:
1) the composition of
boxes inside boxes in a spatial sense;
2) the tendency to fill
the plane (the desertic landscape) with labyrinthine articulations
constructions of passages, niches, rooms that follow similar iterations to the
fractal of Peano, hiding the true accesses to the visitors.
And a higher level of
abstraction exists, that of the non apparent hierarchies, given by the burials
that accompany the royalty and reflect an organizing principle based on the
division of classes. For example, the Inka buried the deads in crypts or caves following the patriarchal
family kins, and the Chimú according to its social class. Although the
governors were placed in constructions with platforms inside the citadels, the
location of the plebeian deads in the suburbian cemeteries, helps to make the
urban form even more complex, the conceptual fractal continues being generated
in other underground planes, and it reaches the tridimensionality, even for
cultivations.
We are before a geometry of non apparent , spontaneous order,
whose capacity is the one of generating diversity starting from simple rules.
This diversity is not arbitrary, because of
having non desirable results, it would have been discarded.
The methodology of
analysis in urban morphology by means of the fractality is a very wide field
and a single ¨narrative¨ will not be enough. We have been interested in the
built environment that is evidenced today in Chan Chan, but the advance in the
archaeological excavations, will guide
us to more complete evaluations by means of the application of mathematical models
based on the theory of the Complexity and fractality; we will be able to
achieve complete reconstructions and recognition of urban morphological models
that include the social order in their relationship with the dimension of the
sacred landscape, the symbolism and the ritual of the deads. And the results will be even more surprising
if we understand the built environment like a great adobe modeling space that as a fractal, has autosimilarity in the
provincial constructions, passing from the monumental and domestic scale in the capital to the minimum scale of the
gardens plantations.
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Pictures downloaded from these web sites:
http://www.turisticalperu.com/domiruth_newsletter12_eng.htm
