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Architecture is the connection between architecture and nature. Organic architecture. Nature is the best source of inspiration for architects

Architecture is the connection between architecture and nature. Organic architecture. Nature is the best source of inspiration for architects

From time immemorial, architects turned to nature for inspiration and introduced its image into individual elements, such as acanthus leaves in a Corinthian capital, a rose window in a Gothic temple, and in any other style there was almost always a floral ornament.

From the second half of the twentieth century, new trends and directions began to emerge, where natural forms dominated the overall design of the building. Metabolism, as a concept that came from biology, has become a new word in architecture. Externally, the building could not be compared with any object of living nature, but it internal structure The architects created a type of living organism consisting of cells, that is, of separate blocks in which a person can live. In the process of life, cells die and are born, and in the case of architecture, it was meant to easily replace old parts with new ones. Appearing in the 1950s in Japan, metabolism left the main architectural monument - the Nakagin Tower in Tokyo. Subsequently, many architects took the cellular structure as a basis, but not all ideas were brought to life. Now this style has faded into the background, but such properties as replacement of parts and complexity in the repetition of residential blocks are still found in modern projects.

Nakagin Tower in Tokyo, Japan

A. Isozaki. CityVair, 1961

HouseVBobruisk, Belarus

ProjectFilene's Eco Pods, Höweller + Yoon,Boston, USA

The next style - organicism - like metabolism, was developed in opposition to functionalism. In addition to the use of natural materials and the desire to integrate the building into the surrounding natural environment, a distinctive feature of organic architecture is also its imitation natural forms, but not at the “cellular” level, but in a broader concept. Asymmetry, curvilinearity, bends bring the building design closer to biomorphic objects. The buildings resemble elements such as tree leaves, sea waves, etc.

In the 21st century, organics have grown into bionics, which is not just an imitation of individual elements, but rather the borrowing of natural forms.

Like the previous styles mentioned, bionics are in opposition. Contemporary high-tech with its straight, unnatural urban structures is recognized as “inanimate” architecture. Many authors are beginning to move from the style in which they previously worked to bionic. They are increasingly collaborating with biologists and engineers to bring their project as close as possible to the desired result. The most famous architects include Santiago Calatrava, Nicholas Grimshaw, and Vincent Callebaut.

ProjectThe Coral Reef,Vincent Callebaut

City of Sciences and Arts, Santiago Calatrava

ProjectThe Eden,Nicholas Grimshaw

Appeal not only to biomorphic forms, but also to the way life works in nature is also becoming a popular theme in architecture. Designed for overcrowded Tokyo, the Shimizu TRY 2004 Mega-City pyramid is the equivalent of an anthill. Such a building with developed infrastructure allows residents not to leave the boundaries of the pyramid.

In 2006, according to a project developed by the Mexican architect Javier Senosyan, a building was built, shaped exactly like a nautilus shell. The uniqueness of this project was the spiral internal structure, corresponding to the natural one.

The project by Spanish architects Mozas Aguirre arquitectos in a sense returns to the theme of metabolism, since the building's plan resembles the interweaving of chromosomes that divide the building's exterior into cells, and refers to the theme of cellular structure.

New projects are increasingly surprising in their closeness to living nature, not only by borrowing forms, but also by developing concepts according to which a particular structure will exist as a separate organism.

To summarize, we can say that the main similarity in the development of architecture and biology is evolution - from metabolism to bionics through cellular structure to the forms of an integral single organism. All three styles opposed the unnatural, rigid geometry of functionalism, and later hi-tech. Today, the distinctive features of metabolism, organics and bionics are often combined together. Modern architects do not stop there, improving their ideas both in terms of visual similarity and design.

Collection output:

NATURE AS THE BASIS OF ARCHITECTURE

Fomenko Natalia Alexandrovna

architect at LLPUSB- Group”, master’s student at the Kazakh Agrotechnical University named after. S. Seifullina, Republic of Kazakhstan, Astana

NATURE AS A BASE OF ARCHITECTURE

Fomenko Natalya Alexandrovna

architect in “USB-Group” LLP, master student of S. Seifullin Kazakh Agro Technical University, Republic of Kazakhstan Astana

ANNOTATION

This article discusses methods of interaction between natural images and architecture. The main ideas of the formation of natural styles over the years are displayed. The influencing factors on the formation of architecture are identified. The work of the influence of nature's working methods on architecture is considered. An option for preserving the natural appearance is presented.

ABSTRACT

The methods of nature image and architecture interaction are view in a matter. Basis ideas of nature style formation over extended time are image. The influence factors on the architecture formation are denote. Works of influence nature system methods on architecture are view. Option of conservation nature image is present.

Keywords: nature; Human; architectural form; ecology design; harmony; adaptability of architecture; landscape.

Keywords: nature; man; architecture form; ecology of design; harmony; adaptability of architecture; landscape.

The connection between man and nature is inextricable; no matter how much a person strives for progress, he still returns to natural sources. Nature is the source from which people have drawn inspiration for centuries, creating new architectural styles. Undoubtedly, they reflect both the achievements of scientific and technological progress and spiritual beliefs. New views, new inventions allow a person to create life around him. Features of the nature of the place, climatic conditions, cultural and historical characteristics of the people dictate the forms of formation of the architecture of recreational areas. The influence of natural appearance on aesthetic education, formation of living values. The ability to preserve nature today for future generations is one of the most important tasks.

Nature is the manifestation of the world in a variety of forms. A unique organism with a harmoniously developed system of interaction between all its elements, one of which is man. A social being with consciousness, intelligence; subject of socio-historical activity and culture. From time immemorial, building culture on communication with spiritual forces. Surrounded by the products of scientific and technological progress, man never ceases to draw inspiration from nature and increasingly strives for spiritual relaxation. What the architecture of recreational areas cannot always allow. The main criterion in design is the economic factor, which is undoubtedly important, but only a competent combination of architecture and landscape creates a favorable recreational environment.

Initially, the term architecture meant the art of constructing buildings; in our time, architecture is a reflection of the capabilities of humanity and achievements in the field of technology. Recently, the most common materials are concrete, glass and metal. New building designs are being developed. Increasingly, the facades of buildings are decorated with metal structural elements, rough forms are used in the architecture of not only business and public centers of the city, but also in the architecture of recreational areas. Filling natural space with architecture with pronounced structural elements leads to the destruction of the image of nature as a single organism. Human domination causes destruction natural monuments. The architecture of recreational areas should serve not so much as an organization of residential processes, but rather be a conductor from the world of humanity to the world of nature, sources of life energy. To satisfy the need for psychological and energetic relaxation, the dominance of nature is important. It is important to be a guest of nature, and not to be its owner. Taking a dominant position, nature invites, gets acquainted, communicates, shares energy, a sense of life, in the case when a person dominates, nature freezes, closes, turns away from the person, it seems to stop breathing, in the hope that the person will not notice her and will pass by. She is waiting for the very moment when the person leaves her forever to breathe easy. At a time when a person can maintain the majesty of nature, be part of the ecosystem. Open a new breath in the formation of architectural styles of recreation areas.

The formation of architecture hidden in the natural environment preserves the pristine appearance of natural monuments. During the formation process it is very important to take into account the interests environment, to obtain a favorable result from the interaction between the environment and man. The location of the recreational zone, climate and ecology of the area play a big role. Following the principles of ecology, the visual solution of the architectural and spatial environment depends on the location. The climate influences the choice of structures and materials used. The cultural and historical factor is also important. The presence of natural monuments requires greater attention to them in order to preserve their appearance. Being a natural treasure of their state, they represent great value in its uniqueness. Taking into account historical and cultural elements in the formation of the architectural environment, the cultural values of the people are preserved. With the advent of civilization, a decline in culture occurs - the price for progress, but looking back in any culture, you can see that the ancestors were in close interaction with nature, that the formation of not only architecture, but also the entire way of life came from natural processes.

The connection between man and nature can be observed in many manifestations human activity. Man's desire to surround himself with living things drives the creation of gardening areas, the domestication of animals and the cultivation of small gardens on window sills. The display of images of nature can be traced in the formation of architectural styles since the twentieth century. Living lines, smoothness and fluidity of forms became the main principles of the Art Nouveau style, the depiction of floral patterns on parquet and the use of plant forms in forging. A style where the decor on the wall smoothly flows onto the ceiling, clearly showing the presence of life inside each element, frozen only for a moment. Expressionist architecture depicts natural forms in its works, most often evoking natural landscapes: mountains, rocks, caves, stalactites. The emergence of the direction of organic architecture was caused by the desire to combine architecture and landscape - the formation of a harmonious space where elements do not occupy dominant positions, but rather closely interact, complementing each other. A style where architecture, while maintaining the constructiveness of the image, is a continuation natural environment, similar to the evolutionary form of natural organisms. Borrowing forms of living nature is observed in the new bio-tech style. The difference is the use modern materials, a combination of glass and metal structural elements. But often architecture, as a structural element, has the function of organizing space to satisfy human needs. A completely different kind of functionality of architecture is displayed in the works of Michael Polin. The use of nature's methods leads to the most unexpected results. Allows you to save energy, resources, and create waste-free production. Nature initially conceived the cycle of substances in nature, which implies the harmonious development of all its elements, but people do not always take this into account. When extracting a resource, a person simply wastes it, making the smallest profit and getting rid of the rest. The same thing happens with nature, often with the development of recreation areas, most of them are destroyed without a trace. natural resource, because the main goal is monetary profit. The remaining nature is killed by pollution. A person considers himself the owner of the land and everything that grows on it, despite the fact that he knows how much he depends on it. Currently, not many projects of “natural architecture” are known. Even in ancient times, living bridges were used in India and Japan; they were created by intertwining rubber trees, the structure being strengthened by natural growth. There are known cases of growing houses using the arboreal architecture method. The directions originated from the direction of arbosculpture created by Axel Erladsen, the meaning of which was the creation of various forms from growing trees. But this takes a lot of time.

Grass roofs are widespread in Scandinavian countries. Norwegian scientists have proven that this type of roofing has excellent heat and sound insulation, which is not only environmentally friendly but also cost-effective. In Germany, it has already become popular to decorate roofs with flower arrangements, which gives not only harmony with nature, but also a special individuality to the building.

A person spends most of his life in the concrete jungle that he creates himself, so recreational architecture requires a special approach and attention. A special role in environmental propaganda and education must be given to promoting a healthy lifestyle in harmony with nature, development ecological tourism.

The idea of human existence in harmony with nature is reflected in many religious movements. Paganism implies full communication man with nature. Every living thing has a soul. The gods are behind all natural phenomena. Communication with nature implies gaining knowledge. Gaining wisdom is a reasonable and caring attitude towards your living planet, returning yourself to balance with the natural world. Buddhism shows the relationship between the processes of the world of spirituality and the processes of interactions of nature. The interaction of energies is considered as physical interaction. Nature is a standard, an open book of knowledge that should be studied. Taoism, like Buddhism, encourages focusing on the present moment, since there is nothing more constant in life than change. The world is what it is, and if perfection exists, it is around us, but not in our imagination. Based on this premise, any attempt to change the world is an attack on its perfection, which can only be discovered in a state of peace. Return to perfection is a movement from the unnatural to the natural.

Architecture is one of the important elements of human life, and since ancient times it has had the function of protection. The harmonious organization of space and appearance is an important factor for creating an environmentally friendly recreational environment. The formation of architecture as a single organism created by man in harmony with nature. Harmony is a balance of opposing forces, an equal combination of interaction, main principle nature. Equivalence of forces is the basis of harmonious existence. Allowing one to penetrate the other and vice versa clearly displays the yin-yang symbol. The search for architecture in nature and the embodiment of nature in architecture is highest degree harmonious interaction.

Bibliography:

1. Concept of environmental safety of the Republic of Kazakhstan for 2004-2015, Decree of the President of the Republic of Kazakhstan dated December 3, 2003 No. 1241. - 19 p.

2. Polin M. Using the genius of nature in architecture. 2010. [Electronic resource] - Access mode. - URL: http://www.ted.com/talks/lang/ru/michael_pawlyn_using_nature_s_genius_in_architecture.html (access date: 03/11/2013).

Organic architecture- a movement of architectural thought first formulated by Louis Sullivan based on the principles evolutionary biology in the 1890s and found its most complete embodiment in the works of his follower Frank Lloyd Wright in the 1920s - 1950s.

Organics (Bionics)(from the Greek biōn - element of life, literally - living) is a science bordering biology and technology, solving engineering problems based on analysis of the structure and vital activity of organisms. Simply put, if you remember Leonardo da Vinci, who tried to build a flying machine with flapping wings like birds, then you will immediately imagine what the organic style is.

The first attempts to use natural forms in construction were made by Antonio Gaudi. And it was a breakthrough! Park Guell, or as they used to say “Nature frozen in stone” - nothing like Europe, spoiled by architectural delights, and the whole world, have not yet been seen. These masterpieces of the great master gave impetus to the development of architecture in the organic style.

In 1921, bionic ideas were reflected in the construction Rudolf Steiner Goetheanum, and from that moment on, architects all over the world took organic matter into their “weapons”.

From the time of the Goetheanum to the present day, a large number of individual buildings and entire cities have been built in the organic style. The most influential representative of organic architecture in Europe was the Finn Alvar Aalto.

Style Features:

● Organic architecture is defined by forms that are not based on geometry. They dynamic, incorrect , arising as a result of contacts with reality. At the same time, each form of organic architecture should be considered as organism which develops according to the law of its own existence, its own special order, in harmony with its functions and its environment, like a plant or other living organisms.

● In contrast to functionalism, organic architecture sees its task in creating buildings and structures that reveal properties natural materials and organically fit into the surrounding landscape. A supporter of the idea of continuity of architectural space, Wright proposed to draw a line under the tradition of deliberately separating a building and its components from the surrounding world, which has dominated Western architectural thought since the time of Palladio. In his opinion, the shape of a building should each time follow from its specific purpose and the unique environmental conditions in which it is erected. IN in practical terms Wright's "prairie houses" served as natural extensions of the natural environment, much like the evolutionary form of natural organisms. The individualism of organic architecture inevitably came into conflict with the needs of modern urbanism, and it is not surprising that the main monuments of this trend were country mansions.

● In its essence, bionics, as an architectural style, strives to create a spatial environment that would, with its entire atmosphere, stimulate exactly the function of the building or room for which the latter are intended. In an organic house, the bedroom will be a bedroom, the living room will be a living room, and the kitchen will be a kitchen. Rudolf Steiner said: “The spiritual aspect of creating bionic forms is associated with an attempt to understand the purpose of man. In accordance with this, architecture is interpreted as a “place” where the meaning of human existence is revealed.”

Attempts at the beginning of the 21st century to transfer the principles of organic architecture to larger-scale structures and to blend harmoniously into nature, creating a psychologically comfortable environment in urban conditions, gave rise to such a style asBio-tech(Bio-Tek) . This style is still at the stage of developing manifestos, but is already starting actively seize positions.

IMAGESNATUREINARCHITECTURE

The development and emergence of new forms of social life, achievements of scientific and technological progress, the introduction of spatial structural systems and effective building materials - all this led to the birth of new properties of architectural form, which, just like the “classical” properties known to us, are involved in the formation of its beauty. At the same time, an interesting process occurs: the tendencies of shape formation in modern architecture (within the accepted concept of “abstract form”, “structure” or “system”) begin to converge, as it were, with the forms of living nature, to approach asymptomatically (never, of course, without approaching) them according to its properties, which are the result of the interaction of function, form and technology.

Aesthetic feelings cause properties that we observe in living nature that are associated with great achievements in architecture, which have passed through decades of scientific and technological progress and the scientific and creative thought of architects and engineers of the 20th century.

These include the outwardly pronounced physical lightness of natural forms with great potential for resistance to mechanical stress; a freely developing space, characterized by diversity and transparency, which promotes deeply penetrating visual observation and holistic perception; structuring of space; alternation of various forms, structures, masses and space with gradual transitions, carried out using the mechanism of the law of differentiation and integration; plasticity of forms; elastic and light bends of solid and wide surfaces, similar to shells made of reinforced concrete and plastics, used in architectural practice; dynamism - both real movements and figurative expression of the growth and development of forms, etc.

Architectural bionics strives to study the objective patterns of manifestation of these properties and find their application in architecture not only for the purpose of solving purely practical problems - design, creation of enclosing surfaces, organization of the environment, etc., but also aesthetic problems associated with the harmonization of function , forms and techniques.

However, not only today, but, apparently, throughout the entire existence of architecture, architects artistically conceptualized, bringing to the level of figurativeness, the above-mentioned properties of the forms and space of nature, often without thinking about the functions that determine them and without connecting them with the latter. And yet, this not only did not contradict the needs and development of the human spirit, but in many cases was necessary for its elevation, for the accomplishment of great social tasks through the means of the art of architecture.

Forms of nature and their spatial combinations became in certain cases prototypes of artistic architectural forms. For example, the motif of lotus thickets was interpreted in the colonnade of Egyptian temples, the forest motif - in the interiors of Gothic cathedrals, which gave them not only expressiveness, but also an ideological mood.

The dynamics of development, growth, and life aspiration in architecture are often symbolically expressed in the form of a spatial spiral, even if this technique is not necessary from the point of view of function (but does not contradict it either). In living nature, a spiral is a functional manifestation of the rationality of the growth and development of organisms: spiral-shaped shells, spiral arrangement of leaves on plant stems, spiral arrangement of petals and flowers, etc.

The problem of dynamics has always worried architects. If now there are technical conditions for constructing really moving architectural forms, then in traditional architecture, when this was necessary, architects sought to express the idea of a dynamic form by illusory means.

Rice. 99. Pavilion of Bulgaria for EXPO-70 in the form of an opening rose flower. Competition project (2nd prize). Archit. Matej Mateev (NRB)

Rice. 100. Monument to Christopher Columbus. Competition project. 1930 Archit. K. S. Melnikov (USSR)

As a result of the practice of architecture, a number of techniques have been developed that help achieve dynamic expressiveness of architectural forms. Modern architects also do not refuse to create images of movement.

In 1969-1970 Bulgarian architect M. Mateev submitted to the competition (and received 2nd prize) the design of the Bulgarian pavilion at EXPO 70 in Osaka (Fig. 99). He took a rose as the basis for the image and gave it the “dynamic” shape of a bud ready to bloom. In this decision of the architectural image, the choice of a rose seems completely justified: this is not a copying of a natural form, but an artistic interpretation of a flower popular in Bulgaria in an architectural work.

When creating the image of the monument to Christopher Columbus (1930), proposed for construction in the area where the crew of his ship landed on American soil, architect. K. S. Melnikov used the “struggle” of two cones: the cone of stability and the cone of growth, symbolically expressing all the difficulties of navigation and ultimately victory. He “inspired” the latter in every sense words, attaching wings to the upper cone (growth cone), which, by the force of the wind, made it rotate (Fig. 100). It is known that in living nature, the “confrontation” of two cones is a characteristic tendency, clearly manifested, for example, in the shape of the crown and trunk of a spruce tree, in the development of mushrooms, etc.

Living nature can evoke even more deeply hidden sensory associations, for example, in connection with the growth and desire of organisms for light, sun, warmth, their vitality - the affirmation of a healthy principle, manifested in fresh and bright colors, in the elasticity of tissues, in certainty and constant the nature of their form - the vital spontaneity of diversity, even seeming chaos (like a city that was formed over many centuries and absorbed the styles of different eras).

Is it appropriate in bionics to use these associations in architectural forms? It is quite appropriate if they are interpreted correctly and do not contradict the humane goals of architecture. The ways of their expression in architecture are suggested by Live nature. Obviously, the use of aesthetic laws of natural harmony cannot completely replace the artistic and figurative expressiveness that is inherent in architecture, as social phenomenon, but the possibilities of architectural bionics here are enormous,

It seems that associative thinking promotes understanding and reproduction of a holistic image, harmony of forms of living nature and architecture. It is especially important for understanding “something” and many changes in forms that often escape the “eyes” of science at the present stage of knowledge of living nature.

This is also noted by the architect. I. Sh. Shevelev, saying that the harmony of form G achieved without connection with associations, does not affect the depths human consciousness, is not addressed to what is stored in human memory. But, I. Sh. Shevelev emphasizes, the art of architecture is characterized not by direct associations that recreate visual pictures, but by associations that awaken moods and psychological states associated with these pictures. In different eras, in different architectures, they are not the same. Ancient architecture, for example, is associated with man, while ancient Russian architecture seems to be associated with images of nature.

Sometimes the question is asked: will architecture, in connection with the use of the laws of the formation of living nature, lose its national identity, which from the point of view of the development of national cultures would not be acceptable.

We are convinced that if this had happened, it would not have been the fault of architectural bionics. On the contrary, architectural bionics helps to find another way to the development of national traits, namely in the aspect of interpreting regional, local forms of living nature in their holistic, spatial ecosystem. The latter constitutes, however, far from being the only, but an integral part of the national environment.

At the same time, architectural bionics does not narrow architecture to a narrowly national one, since many patterns and principles of organization of living forms are universal, not to mention the fact that the use of the laws of the formation of living nature is not self-sufficient and is subordinate to the main one, social function architecture.

Last and highest stage The architectural-bionic process should become a social practice that awakens new needs for bionic methods and can correct old prejudices against them. Architectural-bionic practice is capable of developing and enriching this architecture so much that in fact completely new harmonious architectural-bionic systems, complexes, and urban-planning natural unities will arise.

Culture

Bulletin of the Far Eastern Branch of the Russian Academy of Sciences. 2006. No. 5

V.V.ISAEVA, N.V.KASYANOV

Fractal nature of natural and architectural forms

In order to identify the commonality and specific differences of morphogenesis in nature and architecture, some buildings and structures are considered in comparison with natural forms and fractal models. Architectural forms are more regular than natural ones, and involve a small number of repetitions with their variations.

Fractal morphogenesis in nature and architecture. V.V.ISAEVA (A.V.Zhirmunsky Institute of Marine Biology, FEB RAS, Vladivostok), N.V.KASYANOV (Institute of the Theory of Architecture and Town Planning, Moscow).

Some buildings and constructions are considered in comparison with natural forms and fractal models in order to reveal common and specific features in architectural and natural morphogenesis. Architectural forms are more regular than forms of nature, and involve few iterations with variations.

Over the past decades, a new vast area of interdisciplinary research has been rapidly developing, including nonlinear dynamics, fractal geometry, and the theory of self-organization. An interdisciplinary approach significantly expands the boundaries scientific research, helping to identify common features morphogenesis in living and inanimate nature. Fractal algorithms (rules of construction) in nature and human creativity were discovered by Benoit Mandelbrot. One of the most important characteristics fractal - scale invariance (self-similarity over a wide range of scales). The fractional value of the fractal dimension characterizes the degree to which space is filled with a fractal structure, while the lacunarity value is a measure of the heterogeneity of the fractal structure.

Many processes occurring in nature and society - from cosmic to social and physiological - are characterized by chaotic fractal dynamics. The fractality of natural objects is confirmed by the possibility of constructing very plausible computer landscapes of the virtual world based on simple fractal programs, in which an approximation to reality is achieved by a certain degree of irregularity by introducing random numbers. Plant morphogenesis is also successfully simulated by similar programs. Modeling the morphogenesis of animals at all levels of their organization is a dynamically developing area of biology. Biological structures of complex spatial organization can be quantitatively characterized by determining the fractal dimension, which serves as an indicator of the morphological complexity of these structures. The involvement of fractal algorithms in biological morphogenesis provides compressed genetic coding. Fractal-like structures of living nature are characterized by a limited scale of repetitions and are less chaotic compared to fractals of inanimate nature; As a rule, these are multifractals, i.e. heterogeneous fractals.

Valeria Vasilievna ISAEVA - Doctor of Biological Sciences (Institute of Marine Biology, Far Eastern Branch of the Russian Academy of Sciences named after A.V. Zhirmunsky, Vladivostok), Nikolai Vladimirovich KASYANOV - Candidate of Architecture (Institute of the Theory of Architecture and Urban Planning, RAASN, Moscow).

The use of fractal geometry approaches makes it possible to identify the similarities of a number of living and inanimate objects - both natural and man-made. One example of such parallelism in shape formation is provided by a comparison of the designs of geodesic domes with the organization of fullerene molecules, macromolecular complexes of cells of multicellular animals and skeletal structures of radiolarians (Fig. 1). Geodesic dome building designs were patented in 1954 by R.B. Fuller (1895-1983), an American inventor, architect and philosopher; in our country, such developments were carried out by M.S. Tupolev. Geodesic domes can be formed by a complex network of triangles that form a surface close to spherical (Fig. 1a). The repeated divisions into triangles characteristic of geodesic domes form a fractal algorithm. Designs with such a triangulation partition turned out to be not only promising in architecture, but also very similar to natural forms. In the 90s of the last century, a new substance was obtained - fullerite, consisting of carbon molecules, fullerenes (the etymology of the names of fullerenes and fullerite is very transparently connected with the name of Fuller). Fullerite is an allotropic modification of carbon, the third crystalline form of carbon (the two previously known forms are graphite and diamond). Fullerene molecules are a closed surface in the shape of a sphere or spheroid on which carbon atoms are located (Fig. 1b). The designs of geodesic domes are also similar to some biological structures, for example, macromolecular clathrin complexes (Fig. 1c), networks of bundles of actin filaments in metazoan cells (Fig. 1d) and the skeletons of some radiolarians, single-celled organisms(Fig. 1d).

Fine arts Music also has fractal-like characteristics. Some examples of artists using elements that are repeated at different scales, i.e. fractal sets, given by B. Mandelbrot. Studies of traditional music of Japan, India, Russian folk songs, American blues, music of Bach, Beethoven, Debussy, Strauss have led to the conclusion that music has common features with the dynamics of natural processes, imitating the natural changes of our world over time. A work of art is pleasant and interesting provided that it is not too monotonous and at the same time does not contain too many surprises; music is pleasant if it contains changes in tonality over many frequency scales and changes in rhythm over at least a few time scales. A computer image of the Mandelbrot set can be translated into sounds, resulting in music with repeating and changing “themes.” Translating a human electrocardiogram into sounds produces “songs of the heart,” music synthesized using the algorithm of chaotic fractals of the cardiogram (see).

The use of self-similar forms repeating on different scales, i.e., essentially, fractal rules of construction, is widespread in architecture. The well-known likening of architecture to frozen music (J.V. Goethe) is deeply justified: both music and architecture are fractal. Works of architecture include many length scales and elements of self-similarity: similarity of parts and the whole, subordination of individual elements to the whole (Fig. 2). Architectural fractal structures are more ordered than natural ones. The fractal nature of many architectural forms is very obvious and lies literally on the surface (usually on the facade). Mandelbrot was the first to write about the fractal nature of architecture and cited the architecture of the Paris Opera building, a work of “fine” art (architect Charles Garnier), as an example of fractal creation. M. Schröder cites the Castel del Monte castle, built according to his own design by the Holy Roman Emperor Frederick II, as an example of self-similarity in architecture. This castle has a regular octagon in plan, with eight powerful towers attached to its tops, each of which also has a regular octagon in plan.

Rice. 1. Fractal partition: a - layout of a geodesic dome; b - structure of fullerene molecules; c - clathrin sphere; d - system of bundles of actin filaments of the cytoskeleton; d - skeleton of one of the radiolarians

Rice. 2. Self-similarity of forms in architecture: a - the building of the Historical Museum in Moscow; b - post office building in Vladivostok; c - Indian temple architecture, complex in Khajuraho Fig. 3. Fractal prototypes and architecture of pyramidal facades, bell towers: a - Sierpinski’s “napkin”, built from squares; b - fragments of facades of Gothic buildings in Germany; c - bell tower (Kashira) Fig. 4. Similarity between the outlines of the Weierstrass function graph (a) and the silhouette of the Milan Cathedral (b)

The principles of fractal-like shape formation in architecture have been used since ancient times, but only towards the end of the 20th century, after the appearance of Mandelbrot’s books, the use of fractal algorithms in architectural morphogenesis became conscious. Charles Jenks described the transition to a new paradigm in architecture under the influence of the sciences complex systems, including fractal geometry and nonlinear dynamics. Several key buildings by Frank Gehry, Peter Eisenman and Daniel Libeskind appear to be the first manifestations of this new architectural paradigm. Modern architectural trends that operate with images of complex surfaces, mathematically described by nonlinear equations, can be conventionally called nonlinear architecture. C. Jenks and I.A. Dobritsina wrote about the nonlinearity and fractality of architecture in a general declarative form. B. Mandelbrot's fractal geometry is used to a certain extent for the analysis of architectural forms in the book by K. Boville, the only monograph on fractals in architecture to date, in which a smaller part of the book is devoted to architecture itself. A number of articles and Internet sites have noted elements of the architecture of Gothic cathedrals, the Baroque style, and Indian temples that are repeated at different scales, and an analysis of repetitions in classical order forms has been carried out.

Fractal formalization was applied by Bovill to rows of buildings along streets and to determine the fractal dimension of some architectural structures (including F. L. Wright and Le Corbusier) by the method of counting squares; Such an analysis establishes an aesthetic rationale for evaluating architectural design, allowing recommendations to be made to move away from the deadening monotony of standard architecture. However, attempts to quantitatively link a high value of fractal dimension (reflecting the granularity of detail) with architectural expressiveness do not provide much for understanding the fractal rules for constructing architectural forms. The value of the fractal dimension can only serve as a formal characteristic of the spatial complexity of an object, which does not take into account more important quality characteristics. Although fractals are usually associated with richness of shapes, fractals can also be aesthetically uninteresting, even boring. On the contrary, in architecture there are structures that are practically devoid of fractal characteristics and at the same time very expressive - for example, massive non-linear forms. Fractal prototypes of architectural forms have not actually been shown yet.

The goal of our work was to search for the simplest graphic fractal images that visualize some archetypes of facades, plans and three-dimensional architectural forms, and to involve computer simulation for a qualitative, rather than quantitative, analysis of essentially fractal algorithms of architectural structures - as a rule, not realized by their architects and builders in in terms of fractal geometry. In a broader aspect, this task forms part of the problem of identifying the parallelism of shape formation in such different worlds as inanimate and living nature, on the one hand, and man-made forms - both real architectural and virtual (computer) - on the other. Modern scientific approach using fractal geometry, as well as topology and nonlinear dynamics, is able to identify here many similar directions and solutions of morphogenesis, including previously undisclosed aspects of morphogenesis and the creation of potentially new architectural forms. Referring to Mandelbrot: " graphical representation- a wonderful tool for comparing models with reality,” let’s consider some graphic fractals as prototypes of architectural facades and plans.

Sierpinski algorithm (the so-called Sierpinski napkin, built in in this case made of squares) in the first stages of construction gives a prototype of such religious buildings as step pyramids; vertically elongated buildings of a similar archetype -

temple and fortress towers, bell towers (Fig. 3 a-c). Of course, endless repetitions of any structure in architecture are impossible; real architecture usually contains few repetitions, therefore fractal models that imitate architectural structures (or reveal “ genetic code"architectural objects) are protofractals (Mandelbrot's term for fractal structures with few repetitions). In addition, in architecture, as in music, exact repetitions are rarely found; variations of a theme or image are common.

For the silhouette of temples with many vertical repeating elements, a certain metaphorical prototype can be the graph of the Weierstrass function (Fig. 4 a, b) - a classical fractal function that does not have derivatives at any point (accordingly, it is impossible to draw a tangent to any point on the graph), open V late XIX V. Undoubtedly, the architects and builders of Milan and similar cathedrals were not aware of the function of Weierstrass, and we do not claim that the silhouette lines of the cathedral exactly follow the graph of function - this graph provides only a visual metaphor for such architectural forms.

The Cantor set is another fractal algorithm suitable for describing architectural forms with symmetrically located parts of different heights, which is quite common in architecture (the simplest architectural technique is that a reduced similarity of the entire building rises in the middle part of the building). The fractal structure of the classical Cantor set is discrete, while connected fractals, for example, Sierpinski’s “napkin,” are more suitable as architectural prototypes. The connection of discrete sections of the Cantor set gives a connected fractal (Cantor ridge, Fig. 5b) - a prototype of the “Stalin skyscraper” and similar buildings. The Cantor set with lacunarity variations (Fig. 5c) can be modified in the simplest way, obtaining, for example, a graphic morphotype (Fig. 5c, d), similar to the architectural forms of Indian temples. The fractal algorithm for constructing a discrete Cantor set is similar to the algorithm for forming a dichotomously branching tree - a connected fractal. The inverted dichotomous tree is a generalized “architectural code” of the morphogenesis of skyward religious buildings, the hierarchical structure of which expresses the idea of the presence of higher powers.

The morphogenesis of nonlinear fractals gives rise to the dynamics of images undergoing endless metamorphoses in virtual space, with the emergence complex shapes, similar to biological and architectural. Architectural decor, patterns of lattice and fence ornaments often resemble nonlinear fractals (Fig. 6).

The fractal features of church multi-domes can be examined using the example of a masterpiece of Russian wooden church architecture - the famous Transfiguration Church of the Kizhi Pogost in Karelia (Fig. 7a). A computer model built by one of the authors visualizes the location of the domes of the Church of the Transfiguration (Fig. 7 b, c). The multi-domed wooden churches of the Russian north form a morphologically related series: the prototype of the Transfiguration Church of the Kizhi Pogost (1714) was the Church of the Intercession of the Vytegorsky Pogost in the village of Ankhimovo Vologda region, built in 1708 and destroyed by fire in 1963. The location and dimensions of the domes of multi-domed churches, conventionally shown in one plane of the plan with axial symmetry, in the very general view are reduced to a simple fractal algorithm of the Sierpinski “napkin” variant (Fig. 7d).

One of the universal fractal algorithms, spiral, widespread in non-living things (from trajectories elementary particles to cyclones and galaxies) and living nature (shells of mollusks, horns of ungulates, curls of plant shoots), as well as in architecture and design (Fig. 8), gives many similar solutions to morphogenesis. Three-dimensional implementation of spiral decor in the form of parallel or unwinding

counter directions and intersecting spirals are embodied by the heads of St. Basil's Cathedral (Fig. 8a). "St. Basil's Cathedral is a bizarre fractal of the golden ratio, defined by at least eight terms of the golden ratio series." The chords of golden proportions and other fractal relationships create the architectural symphony of this temple.

Architects know such implementations of the three-dimensional spiral algorithm as the Tatlin Tower (a model of the monument to the Third International) and a similar design of the spiral completion of the building on the Patriarch's Ponds (Fig. 8e).

A visual interpretation of the “golden section angle” is given by a fractal algorithm, manifested in living nature, ornaments and architecture. The computer-generated image of a “sunflower” (Fig. 8b), where a step equal to the “golden angle” is used as an angular increment, is very close to the real picture of the location of sunflower seeds (Fig. 8d), which is less ordered compared to the ideal computer model . A similar arrangement, called phyllotaxis (phyllo - leaf, taxis - movement), is typical for leaves on the stem (or their derivatives), for scales of coniferous plants; in this case, the number of rows twisted in one direction and the number of rows twisted in the other direction constitute two adjacent Fibonacci numbers. On Sat cellular level a similar feature is manifested in the arrangement of tubulin dimers in microtubules - cytoskeletal structures.

The simplest and most general three-dimensional fractal model of far from beautiful typical box buildings can be Menger’s “sponge” (Fig. 9a), the structure of the internal space of which is shown in Fig. 9b. In the most general form we can say that the rectangles of the windows are like a whole rectangular building, and the parallelepipeds of the interior are like the entire “box” of the building. Undoubtedly, even the most primitive panel house is not built exactly according to Menger’s “sponge” algorithm, but fractal geometry includes objects whose element, repeated on different scales, can be further deformed and changed in accordance with the multifractal construction program. A fractal building can be constructed from parallelepiped bars (and include parallelepiped voids), which can be shifted, rotated, compressed: fractal algorithms allow compression, rotation, and nonlinear transformations of the original shape. With the chaotization of such algorithms and a certain accumulation of transformations, forms similar to the architecture of postmodernism and deconstructivism emerge.

So for different types architectural structures, you can find a fractal analogue, two-dimensional or three-dimensional, and thereby identify their fractal algorithm. Model fractals such as the Cantor set and the Menger sponge can serve as quite adequate models of architectural morphogenesis. Of course, unlike relatively simple and regular geometric and computer fractals with infinite

Rice. 5. Cantor set as a prototype of architectural forms: a - Cantor set; b - Cantor comb; in - Cantor set with different lacunarity; d - its simplest transformation Fig. 6. Nonlinear fractals and similar decorative forms of metal fences: a, b - Julia sets; c - fragment of the Mandelbrot set; d - pattern of the balcony lattice of the Vladivostok GUM; d - lattice gate leaf in the Rococo style in Wurzburg, Germany

Rice. 7. Church multi-domes and fractal model: a - Transfiguration Church of the Kizhi Pogost; b, c - computer model of this church: fragment of the facade (b), fragment of the roof plan (c); d - variant of Sierpinski’s “napkin”

Rice. 8. Spiral algorithm and forms of nature, architecture and design: a - St. Basil's Cathedral; b - computer model of phyllotaxis; c - logarithmic spiral; d - sunflower phyllotaxis (for clarity, some seeds have been removed); d - spiral pattern of the fence (Ryabushinsky’s mansion in Moscow); e - spiral completion of the building on the Patriarch's Ponds

Rice. 9. Three-dimensional model of Menger’s “sponge”: a - appearance; b - structure of the internal space

repetition of the same form, in architecture the rules of construction are applied using a limited number of repetitions, changing the rules of their construction, violating strict similarity by introducing many variations, i.e. protofractals, multifractal and irregular algorithms are used.

As a rule, the search for formulas of harmony and beauty of architectural forms is carried out during the analysis of creations already created by outstanding masters. It is known that the idea of the famous golden ratio, used by Phidias during the construction of the Parthenon, appeared two centuries later in Euclid’s Elements, and the term itself “ golden ratio” was introduced by Leonardo da Vinci more than a thousand years later. Both the use of fractal rules of construction in architecture since ancient times and the use of the golden section, of course, were not conscious in terms of later concepts and did not always turn out to be mathematically verified; In the search and creation of artistically expressive proportions, the architects were guided by their intuition and sense of harmony. And in our time, architects do not always realize the ubiquity of the fractal construction of architectural forms, just as Moliere’s character did not know that he was speaking in prose.

The fractal approach is not a panacea, as Mandelbrot himself wrote, and not at all new era in the history of mankind, but only new, but quite effective method analysis, and potentially the design of architectural forms, which can significantly enrich the language of architectural theory and practice.

The famous Spanish architect A. Gaudi gave a new interpretation of Gothic forms in his Cathedral of the Holy Family (Sagrada Familia) - forms similar to natural ones; Gaudi abandoned Euclidean geometry, symmetry and regularity. The fractal-like shapes of the cathedral, like a sand castle, are represented by the chaotic, irregular fractals found in nature. Modern representations nonlinear science gives rise to a new concept of the relationship between order and chaos as a state that includes elements of unpredictability, irregularity, and mystery, similar to the richness and uniqueness of natural forms. The use of the concepts of nonlinear dynamics opens up the prospect of a correct analysis of the relationship between regularity and irregularity, randomness, and asymmetry. The aesthetics of nonlinear forms with elements of chance are formulated by G. Eilenberg: “Why is it that the silhouette of a storm-bent tree without leaves against the background of the evening sky is perceived as something beautiful, but any silhouette of a highly functional university building does not seem so, despite the efforts of the architect? ...Our sense of beauty arises under the influence of the harmony of order and disorder in natural objects - clouds, trees, mountain ranges or snow crystals. Their outlines are dynamic processes frozen in physical forms, and a certain alternation of order and disorder is characteristic of them. At the same time, our industrial products look somehow ossified due to the complete ordering of their forms and functions, and the products themselves are more perfect, the stronger this ordering. Such complete regularity does not contradict the laws of nature, but we now know that it is atypical even for very “simple” natural processes. Science and aesthetics agree on what is lost in technical objects compared to natural ones: the luxury of some irregularity, disorder and unpredictability.”

The trend of organically integrating structures into the natural environment, the integration of natural and man-made landscapes is manifested in the similarity of lines, surfaces and shapes in architecture and design to natural forms. This trend is clearly expressed in the Art Nouveau style and “organic” architecture. Widely used at the beginning of the 20th century. in Art Nouveau architecture, plastic, “flowing,” asymmetrical, biomorphic lines, surfaces, “flowing” plant decor, and relief images of heads give buildings a resemblance to a living, developing organism, imitating the irregularity of natural forms.

Architecture of the late 20th century. The use of biomorphic metaphors is also typical - anthropomorphic, zoomorphic, phytomorphic, as well as plastic geomorphic forms, as if growing naturally from the earth, with the organic integration of architecture and the natural landscape. In our time, there is a deeper awareness of the unity of the natural and anthropogenic environment and the unity of the principles of formation in “living” and “inanimate” nature, supported by the concepts of nonlinear science. The modern scientific approach can be successfully applied to search for architecture, adequate harmony of order and chaos of the natural environment, architecture that can become a semantic dominant in the natural and historical context, the spirit of the place (genius loci).

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