Vol. 6, No1 ( September
2001)


___Oxana
Makhneva
Yekaterinburg 

Fractal
Semiology 

Connection between
production and perception is the first problem for an architect, because
architecture as an aesthetic practice should find a way for materialization of
a creative concept. The concept is an idea. Hegel supposes that it’s impossible
to present an idea by means of geometric figures. However, the thinker believes
that the natural forms and combinations of colours represent an embodiment of an absolute idea.
Consequently the
principles of nature organization are the methods for transformation of the
architectural concept into reality.
In 1970s (nineteen
seventies) the mathematician B. Mandelbrot defined the nature’s principles as
fractal principles. In other words, all natural forms are fractals, for
example a leaf of a fern, clouds, coasts, etc (fig.1). Contemporary
investigators state that the world order exists or is formed as a global fractal Mavrikidi Ph., 2000:32).
Principal characteristics for
fractals are selfsimilarity in any scale and dynamic development that aspires
for infinity; therefore a fractal is a model of any dynamic system.
Consequently, a semiosphere is a global fractal too and in this case we should consider the language of architecture as
the fractal. In fact, a production of sense is a predication. At present, the linguistics defines the predication as a multitude. The
question is a multitude of possibilities and any possibility is communication
with an information field that is the predication is the formula with several
variables (fig.2).
In accordance with the
fractal theory we can say that the formula of
fractal generation is the predication. In fact, the fractal is a complex
number. In other words, this is a point that is
constantly changing coordinates and its
coordinates of the point depend from special parameters. These parameters
represent a code of fractal generation and these parameters are variables of
predication formula, which depend from peculiarities of information. One can
say that Logos creates the order in chaos according to the fractal production,
Mandelbrot himself emphasizes that the fractal theory is a study of order in
chaos.
According to Yuri
Lotman’s theory, we comprehend architecture as a text (Lotman Yu.,
1996) and predication as a notionclue for production of this text, and then
the fractal becomes a visible predication of an architectural idea. So, we
study the fractal as a logical image of a real architectural project. A visible logical image offers a material
for perception, because the sight is the basic source of perception. Creation
of a fractal permits us to test the future project by means of perception.
Besides, we can test a real object by means of creating its fractal.
The process of fractal
generation consists of three stages. The first stage precedes creation of the
fractal.
If our purpose is to study the existing
architectural situation, we measure perception of the real architectural space;
in other words, we investigate the sign system in terms of pragmatics. The perception
of architecture determines behaviour; therefore, fixation of people’s behaviour
in an architectural space indicates the quality of architecture. The negative
behaviour designates a defective predication that is the predication formula is
in need of correction.
Consequently
we should construct a defective fractal and compare it with a model fractal.
If we plan to construct
a new object, we begin with model fractal.
The parameters of any
fractal are colours, coordinates of the initial point, type of fractal and
quantity of iterations. The predication formula is connected with the Base of
Knowledge and any element of this Base proposes the parameters, in other words, an element of the Base has
colour and voice and it offers a quantity of iterations for the fractal. It is
necessary to specify the status of the elements of the Base of Knowledge. In
his work «Sein und Zeit» Martin
Heidegger speaks about the temporary essence of the existence (HEIDEGGER, Martin,1993:45). So any knowledge
belongs to the history and the Base of Knowledge is a complex of the historical
facts. We reveal some basic types of historical document; namely: legends,
businessdocuments, legislative documents and memoirs. All the types have voice
and colour, for example, businessdocuments are dark blue, and legends are
yellow colour.
type of information ↓ 
paramEtres of the fractals 
notion ↓ 

line ↓ 
function


quantity of iterations 
colour 
choosing
of palette 
We determine the colour
and line by means of an experimental method, that we call a semiometry. The
semiometry is coding of information by means of utilization of associations,
that is a revelation of causality between different sign systems, for example
between the architectural quality and behaviour, between the notion and colour,
etc. Therefore, we begin with the definition of one characteristic of the
information and this characteristic in its turn, defines other characteristics
by means of associations or adjacent notions. We reveal semiometric dependences
that are a method of production of a seme. The fractal is a synthesis of the semiometric
dependences; therefore the fractal is visualization of the organization of the
seme. In other words the fractal is the visualization of isotopic connections (LEFLAIVEVERNET, 1999:326). In this case the seme is a minimal unit of
architectural text.
For example we determine
the businessdocuments as authentic information, while the legends are not
authentic. Thanks to semiometry we characterize the authentic information by
means of adjacent notions. The notion of the authentic information corresponds
to the notion a «loud voice».
The «loud voice»
corresponds to the notion «rigidity» that in its turn corresponds to dark blue
colour according to the research in the field of phonetic characteristics of
colours. According to semiometry the rigidity is signified by means of direct
line. So, the view of fractal depends on information.
Moreover, we estimate
the quality of information and authenticity of its sources. All these
characteristics become parameters of fractal algorithm; therefore, the fractal
becomes a synthesis of many elements of the Base of Knowledge. The colour scale
depends on the quantity of participants; besides, the combination of colours
creates a melody of fractal. It is necessary to note that the type of
architectural space defines importance of each of informants, for example a
religious space proposes activization of the legends and the memoirs that is
logic image of such space exists in yellow red colour scale. The type of
architectural space is an attribute of space and the attribute offers
parameters of the fractal.
If we correcte the real
architectural space, we create two fractals namely the fractal of the correct
predication and the fractal of the defective predication. We photograph people
and we analyze their behaviour. If the behaviour is negative for space we make
a conclusion that the predication is insufficient. For example, if people
leave, if they do not want to stay we say that a logical image of the space is
not harmonious. In other words, the fractal is not beautiful because the melody
is not pleasant for hearing and the colours are not pleasant for sight.
Thanks to the method of
the semiometry we find the connections between morphological structure of space
and behaviour. We make the semiogram and each point is morphological unit, for
example a building, a street lamp, a bench, etc. (fig.3).
We use a matrix to
estimate the functional and aesthetic quality of architecture. Each unit has a
zone of offer and this zone depends on the architectural quality, in other
words, the architectural unit offers a mode of behaviour. The response of the
society to the offer of architectural space is different. ”The response” is
activization of the offered type of behaviour. In other words, it is
communication of architectural unit with a society. We call this communication
a valency of an architectural element. We have created a periodic system of
architectural elements and the valency defines the necessity to improve the
architectural quality. If the type of negative behaviour is activated outside
of all zones of the offer, we should create a new architectural element. For
example, we analyze religious and museum space in a city and we notice a
negative response of the citizens, an absence of interest and a desire to leave
the space.
In this case the
predication is defective, in other words, information supply is insufficient.
In this case the fractal is the logical image of negative behaviour and
negative emotions. The legends are the most important element for religious space. We study local folklore and we learn that
the given space is the place where the emperor Nikolai II and his family were
executed. The spirit of this place is spirit of tragedy, which waits for an
opportunity for a materialization. Therefore, the architects plan to construct
a church that is a monument to the emperor. We call the church’s fractal
”Ringing of the Bells” (fig.4).
”Ringing of the Bells”
is the fractal for correction of emotional conditions of this space. We use the ”ARCHITECTURAL FRACTING” program
for the creation the fractals.
So, the second stage of
the fractal process is fracting when the program creates the fractal that is
coded information about the architectural concept.
The next stage is a
postfractal analysis. During this analysis we use the semantic potential of
lines, colours, sounds and silhouettes. We use the research of Professor
Barabanov for postfractal analysis (fig.5).
In this research lines
are presented as emotional vectors. For example, the horizontal line signifies
equilibrium, satisfaction, and monotony. The vertical line signifies nobility,
drama, inspiration, development; the zigzag is rough, the point is an
embodiment of stabilization, etc. (BARABANOV, 1998:124).
The colours are notions by analogy. It is
possible to say that the fractal gives a basis for the production of sense and
consequently the production of forms. An irrational basis of sense is the
principal method of Futurist poetry. The combinations of sounds without sense
create sense and cause an image of colour and lines. The correct logical image
should ensure connection between production and perception, i.e. conformity
between the image fixed in the language and the influence of this image on sub
consciousness of the spectator. The problem is to find connections between
production and perception of forms. A
considerable difference between the production and the perception leads to
destruction or modification of the form. The characteristic example is change
of an executer’s place of the emperor by means of construction of a church.
The fractal ”Ringing of
the bells” gives the principal notions for the conception of the project
”Worship way”. The ”Ringing of the bells” is grandeur, a reminder of the
tragedy and expiation. So the silhouette of an underground bell symbolizes the
past, the star sky is grandeur. The fractal is a logical image of the ”Worship
way” project (fig.6). The red colour symbolizes the tragic past of Russia, the
green colour gives hope for a new life.
The fractal has influence
on sub consciousness as a synthetic combination of all factors that are the
phonetic characteristics, the lines and colours.
Therefore, the fractal
gives a powerful creative impulse and we use the ”ARCHITECTURAL FRACTING”
program is introduced into the educational process and the process of creating
competitive design projects.
For example, the fractal of the project ”Sea star” proposes the architectural concept. The ”Sea star” symbolizes the patron saint of the seaman and the conceptual words are a thoughtful mood and contemplation. The large aquarium in a penthouse is a symbol of a ”pearl in shell” that is a symbol of the patron saint (fig.7).
So the fractal gives the possibility for the visualization of the invisible information and a synthetic organization of a language unit. In fact, the logical image exists thanks to the algorithm that is the predication formula; therefore, this logic image is a result of deliberate work with semantic potentials. The fractal translates invisible information into a zone of visible images and rational information influences sub consciousness by means of irrational impulses. The architecture as aesthetic practice is in need of combining the rational and intuitive sources. The fractal semiology studies perception as a basis for production, as the beginning and the end of a creative process. The fractal as the logical image permits us to use the emotional argument for production of forms.
In our laboratory we
created the program for fractal music. This music depends on fractal parameters
and we receive musical argumentation for production of forms by means of
fractal music. For example, the music of logical image ”Ringing of the bells”
is a profound sound that is an embodiment of past. The tender ring is hope for
future.
In the space of the
semiosphere architecture exists as a text; therefore, we examine the formation
of the language. The language units are organized as dynamic system, which live
and are constantly changing. However, the laws of formation of any unit are
similar to those of all systems. The combination of dynamic, accidental and
stable is an organizational principle of order in chaos. According to the
expert’s opinion, the fractal is the most effective, if not the only, way of
penetration into the laws of chaos.
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