**Urban Evolution Analysis Method Using Self
Organizing Dynamic Model.**

** **

**Dr. Adolfo Benito Narváez
Tijerina.**

*Facultad de Arquitectura,
Universidad Autónoma de Nuevo León, México.*

*Email: **anarvaez@far.uanl.mx*

* *

* *

**Abstract:**

The
focus of this work is centered on application of urban ecology analysis to
comprehend the urban evolution. Describes the analysis method to know how much
the environmental variables on an urban land interact. This information serves
as a basis of a simulation model of urban evolution. As a conclusion analyses
the philosophical implications of the method in face to deeply understand the
correlations between social and physical spaces in the city.

** **

**How can be an urban evolution predictive model (UEPM)?**

The UEPM can be defined using a variable correlation
matrix being this as a system equilibrium. In fact, the matrix shows the state
in which the system is found in a given moment of its history. As I. Prigogine
[1] state, we look that the urban system is itself far away from equilibrium,
Like the Russian scientist says about dissipative system that rise from the
fluctuation of elements that leads the disequilibrium, therefore leads to the
beginning of the self organization process.

It is possible to define an effective media to create
the evolution of this system in time with the cell automata, from the middle
state of the system (the system equilibrium) which is defined by the
correlation matrix. Such matrix represents the correlation degree of the environment
variables, in this case the path in which different aspects of form and space
is used and urban forestation correlate. The equilibrium- non equilibrium can
be defined by the matrix in a proportion terms, meaning the different forces of
environment interacting upon the cells. From this two questions rises: What and
How can be defined as a cells in this particular system? And the other is, how
the cells changes toward the system equilibrium?

In the cell automata, the cells are the minor division
in which each component of the system works keeping its distinctive
characteristics; the microscopic elements define this units, that works on a
macroscopic scale and react as unit. As Prigogine [1] says, in the evolution of
this self regulated systems is possible to observe that the time divides the
macroscopic components more precisely each time (after a qualitative jump that
the system suffers from a fluctuation that rises the critic horizon of
equilibrium, that the cell system states), whit this, the interchange process
of each cell with it’s environment accelerates the evolution process of the
system as a whole, because the fluctuations are more frequents every time. In
this way, the system can be absorbed by the environment (recovering the
equilibrium “entropic death”) or jumping to another state being the nuclei of a
new compound organization in its initial states from a gross cells that will
become to states of more complex organizations.

We study the basic cells of the urban system are the
individual properties as defined by the Public Property Registry Office. It is
possible to state that the morphology, land use and urban forestation are
attributes that changes quickly with the time but these changes occur upon a
constant pattern.

The cells as we see have an edge (property limits) and
some attributes which are the variables that we define before in order to build
the matrix correlations these associated to each cell fluctuates according to a
interchange of information process with environment, in this case the next
neighbor (laterally or frontal properties in the street). What is this
interchange? Prigogine [1] states that the relationships of each cells of the
dissipative system with its neighborhood are given in the imitation or non
imitation process of the human systems.

In this way we can think that the variables will
changes with the time by the imitation of its neighbor cells or react in the
opposite manner. Let say that each land use has a different color we will see
how in a self regulation process will form groups more or less thick, until few
colors dominate in the system, and the system became homeostatic and this can
be compared to a thermodynamic death. And less we provoke a fluctuations in the
system –architectural development, urban works, public development (lets say a
road, transport system, park) and this can will put to play another dissipation
process of a new self regulated system that will revitalize the dead urban
environment.

This process however is not that simple, lets say:
making an urban evolution simulator that only takes the imitation or non
imitation process of next neighbor, this is right for a static system that
raises the critical horizon of the system. In Monterrey file the correlation
matrix reveals the state system upon a time is like a picture of the
environment in a moment of its history, that changes very slowly being the
portrait of one step in the dissipative system evolution, this defines the
subsequent steps. Our hypothesis is that the matrix is like a resistant force
of change and will put a measure to the transformation possibilities of
environment. The imitation and non imitation can be defined as a two
contradictory forces that the cell faces in its evolution, let say in a vector
diagram the origin if the two forces is the center of the system and disposed
over the same axis there will be another force that will be opposed to both in
a perpendicular axis, and the result of this diagram represents the
probabilities of the self fluctuations in the dissipative system. Let us
complicate this a little bit more. In the environment it is found a specific
proportion in the attributes distributions (variables) associated to each cell
and we define this by the next formula:

(V_{B1}) k

rV_{B1 }=
__________________ + W

n[V_{B1}, V_{B2}... V_{BN}] (1)

rV_{B1}; proportional
distribution of the attribute

(V_{B1}); is the number
of cases in what V_{B1} appeared in the category B

n [V_{B1}, V_{B2}... V_{BN}]; is the simple arithmetical
addition of the cases that have V_{B1}, V_{B2}...V_{BN}
in the category B

k is a number to normalize the
result upon a base of scale, for example a percent where k=100

W; is the amount of “local energy”
and its non homogeneous level on the environment normalized in a percentile
level (2 formula).

This proportion states that each
cell will fluctuate from one direction to another. Do not forget that is
possible that a high proportion of system attributes can mean that the system
in this moment it is in a non equilibrium state by an attribute fluctuation
associated, this has a potential to impact the whole system and lead to a new
equilibrium based on the attribute, if this fluctuation overcomes the critical
horizon. Now, let us say that these probabilities are vector forces that are
opposite to imitation or non imitation forces and the system state as another
force opposite to both we have the components to calculate the probabilities of
the self fluctuations.

High or low level of correlation
of the system variables state a superior force of resistant to a change,
meanwhile a level near to the middle of the correlation scale will mean a low
level of resistance of the environment, in this way each attribute should be
compared first in correlation to others attributes of the cell, and then
calculated the transformation probability level. A global calculus that takes
to account the statistical toward the changes or non changes of the total
system can indicate the system evolution potentiality. The figure 1 shows the
way of this calculation upon the environment transformation probabilities. R
represents the system resistance, which is a measure of system variable
correlation value minus a W factor, which is a
constant in (1) and (2) equations that defines the “local energy” and its non
homogeneous level in the environment. W is an empiric quantity, it is possible
to imagine W as a differentiate land value in every locations of the urban
system. Each cell in the process of change, take W from the environment and
translate it to another cells of its proximity. It is possible to think that
when this process occur, merge a new type of W, produced by each cell in it. In
this case, W transforms in an additive factor in the interchange equation of
system evolution. Because now we are already searching about this phenomenon,
we do not have an adequate idea of this process.

To know the amount of system resistance you can apply
the next formula:

R= PH_{1} [A UV_{B1...BN}] – W (2)

* *

R; is the system resistance to change

P_{H1} [A U V_{B1}...V_{BN}];
is the correlation hypothesis distribution in A field into V_{B1}...V_{BN}
when Ho is normalized.

The imitation or non imitation
represents the conflict probabilities rV_{B1…}rV_{BN } and is a function that varies with its magnitudes in a mirror like
fashion being the probabilities the positive and the back probabilities the
negative aspect, being exact in its measurements. In this way it is possible to
calculate the system fluctuation tendency until you have the critical horizon
of the system that leads to a major non equilibrium. The back probability
stabilize the tendencies establishing that the cell go for the non imitation
leading to another pattern or fluctuation.

Now, with these attributes
proportions in the environment that you can graph as a two dimension diagram
you have to add the system state for each cell type and represents the level of
variable correlation. Then with the correlations scale now is possible to get a
new scale in which the odds would be equivalents in size and the middle of the
scale is equal to 0.

With this data you can have a
tendency for each cell system attribute and the measure can be obtained by the
next formula:

T= (r_{VBN})^{2} + (R)^{2 }^{ }(3)^{ }

T; equal probability of
attribute transformation in the given cell

The transformation probability
in this case always is a higher number than the system resistance which is the
way where the systems fluctuates to equilibrium, in other words when r_{VBN} values get equal (unique
variable) and R, reducing the matrix to a single component, in other words 1x1
matrix where T is equal to any value, the system will meet equilibrium in an
entropic dead fashion[1].
This is because the m value defines the tendency toward changes, because when
the magnitude is equal to 1 the system will meet equilibrium: no attribute can
overcome the critical horizon and therefore it would not get an isolated state,
but when the value is greater than 1 the system will have an strong tendency to
change. You can have horizon level fluctuations. This level, defined by m, will
appear by the system inherent characteristics and is self regulated. The
fluctuations act by them, so the fluctuations will appear by the simulation
itself and not from previously established parameters, m only points a
tendency. When m is less than 1, you will have a situation where transformation
is less like, and there is a great resistance to a change induced by the
attributes correlations of the environment.

rV_{BN}

m=

R (4)

* *

m= is the way where the
tendencies goes

m is a value that is helpful to
define the attributes of cell fluctuations. We can use m value to point out the
attributes with great tendencies to a change. This calculation will be done in
the way of imitation and not imitation as a mirror like values defined by rV_{BN}. In a dynamic system each new
change is associated with a new system of equilibrium and the T, m, R and rV_{BN} values vary reciprocally these are
strongly dynamic values chained by mathematic operators. So the simulator will
have to do global calculations that will interact with local calculations.

We have to mention that there
are some exotic attributes that merge from uncommon patterns in the system.
What is the tendency of the exotic patterns of the system? How much is bounded
the isolated system with its environment (cosmopolitan city, citizens with lots
of information not related with their environment)? If we transform this
variable to a number that means global chaos-order, we can generate a
simulation with exotic attributes. This number can be related with the level of
variety in the environment meaning that the value is equal or greater than 1. 1
means all the cells are equal and greater than 1 all the cells are different from
each other.

A system like this can be helpful when you are
evaluating a new architectural or urban project toward its environment, put to
interact with the rest of cell systems analyzing any merging variable that can
be produced, what effects will interact in other subsystems. Also it came be
helpful to understand the equilibrium or non equilibrium state that acts on a
urban system in any moment of time, so you can act in order to revitalize the
system. In many cases you can avoid a miscalculation before the things are done
and prevent mayor financial looses. And finally this is what you have to avoid.

The method we developed opened a set
of questions to the research that nowadays it has become search axis. The
stronger question has to be with the conceptual articulation of the physical
and social space. We mentioned at the beginning of this article how the
correlation of the physical and social space seemed to emerge of the metaphor,
which was created by means of the language respect to a parallel world with the
space of action in order to the new conceptual world would live
there, claiming objectivity. So, the
site in what something is in the world would belong to the social *localization*,
hierarchy of the building or zone to social *rank. *It seems to each
physical space attribute could belong another one which would define it (almost
in the same semantic way) some social space attribute.

So, we assume that the localization
is a parallel value and were watched directly; also we built an instrument
which would measure the correlation of the physical and social space,
subordinated to this shared attribute. The creation of the analysis instruments
that look for the correlation of the physical and social components through of
other attributes shared by these without a doubt will be the new task of our
research team in the future.

**References.**

[1] PRIGOGINE, Ilya (1997). *¿Tan sólo una ilusión? Una exploración del
caos al orden*. Barcelona, TusQuets.

[1] The T value is always positive
because this is one of the dissipative system characteristics and this one
defines time for it and is irreversible, this means a permanent tendency to
change in the self organized systems.