(Published in Spanish in Contextos 11. Personal translation)
ANALYSIS OF DYNAMIC SYSTEMS AND VERIFICATION OF THE RESULTING URBAN MORPHOLOGY
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
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 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.
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
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
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
