Vol. 6, No1 ( September 2001)
___Oxana Makhneva
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 (nine-teen 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 self-similarity 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 notion-clue 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, business-documents, legislative documents and memoirs. All the types have voice and colour, for example, business-documents are dark blue, and legends are yellow colour.


type of information

paramEtres of the fractals










quantity of iterations


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 (LEFLAIVE-VERNET, 1999:326).  In this case the seme is a minimal unit of architectural text. 

For example we determine the business-documents 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 semio-gram 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 post-fractal analysis. During this analysis we use the semantic potential of lines, colours, sounds and silhouettes. We use the research of Professor Barabanov for post-fractal 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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