The contemporary usage of fractals in architecture has resulted due to a range of varied concerns. One of the concerns is the organic metaphors of design as used by Peter Eisenman and Zvi Hecker. Peter Eisenman exhibited his House 11a for the first time in The overall geometry is taken from a sunflower, which connects snake- shaped corridors, mountain-stairs and fish-shaped rooms.
This is once more the concept of fractal geometry: to get a complex object out of simple rules or algorithms. Methods of application of fractals in architecture The application of Fractals in architecture can be usually done in following different methods: 1. Conceptual method: This uses fractal geometry and its concept as a guiding element to its theories. This method provides a theoretical solution that ultimately influences the final form.
Geometric-mathematical methods: which uses scheme of counting squares to calculate the Fractal dimension. This method is used to analyse the existing building also. Geometric — intuitive method. This uses the geometry as inspiration for creative expression [4].
Two-dimensional fractals in architecture I start off with an overview of two-dimensional fractal forms in architecture, which are mostly present in the ground plans of buildings. This application can be found in a wide range of architectural structures, ranging from the plans of fortifications, to the organization of traditional Ba-ilia villages Zambia Figs.
The global form of the latter settlements reoccurs in the family ring, which consists of individual houses, which are, again, similar to the overall shape of the village [14]. Most of the ancient African settlements exhibit fractal characteristics.
These intuitive choices of fractal geometry by the ancient settlers show the relevance of fractals with respect to habitat building. Here they practiced an extended family system, which was housed around a ring shaped livestock pen. The pen had a gate at the front and storage houses around it. The buildings became progressively bigger around the ring. A definite status gradient is thus established. The entire settlement is also a ring that constitutes of smaller housing units as described above.
Wright often applied this procedure to his work. Initially, the geometry governing his architecture created with the aid of such modules remained Euclidean. In later works, however, these elements were sometimes so organized that they gave the building a remarkable fractal organization.
The Palmer House seems to be the culmination point of this evolution. Here, one geometric module — an equilateral triangle — is repeated in the ground plan on no less than seven different scales [14] Fig. On first sight, the link with fractal geometry could seem obvious: such patterns are rich in detail, which is an intrinsic characteristic of fractals [14].
The contemporary architectural group Ashton Raggatt McDougall was perhaps one of the first to apply fractal tiling to architecture.
Storey Hall - Ashton R. This design for a public space to mark the centenary of the federation of Australian states an important step in creating a nation from its parts is a story that reflects at every level the shift in geometry from top-down to bottom-up, encapsulated by complexity theory and fractal geometry Figs.
The fractal self-similarity of the panels became a vital quality in achieving coherence and difference to the facades. The facades of those buildings that define the public spaces, include an almost iconic representation of self-similarity: V5 triangles that combine in fives to create larger triangles and therefore, five of these into the next scale of the same proportion.
This is an intellectually graspable and simply constructible motif, that is nevertheless combined in ways that generate relentless difference and absence of repetition across the whole site [1]. The variation between the internal and external patterns and between the elements that link their nodes creates, in the steel square sections that mark these geometrical etchings, a boscage through which light is filtered in a way that is powerfully suggestive of the complexity or organic precedents cited by Benoit Mandelbrot as calling for fractal geometry for their description [1].
Another example of three-dimensional fractals in architecture can be seen in Grand Egyptian Museum in Cairo, Egypt Fig. Plateau Edge was designed as a vast, sloping, translucent stone wall, inscribed with fractal patterning. For its subdivision, the wall adopts a fractal described by Waclawsieve or gasket, triangle.
The design is dominated by the sightlines from every gallery to the pyramids, whose rigorous geometry informed the design, conception and the adoption of the Sierpinski triangle as the motif for the wall. Centenary of the federation of Australian States [1] Fig. Grand Egyptian Museum in Cairo, Egypt [1] 'Fractile' is a term coined by the design team for the scale less, self-similar patterning of the building surface, deploying Ammann aperiodic tiling Figs.
In the Ammann set used, there are three differently shaped tiles Figs. Each one of those three tiles can subdivide perfectly into copies of the same three tile shapes, scaled down exactly by the Golden Ratio. Each time a particular tile of the set of three is created - the 'R' tile - the subdivision is stopped for that tile.
This creates a fractal that is especially rich because it, too, is aperiodic, and does not repeat in a way that would allow it to be mapped to itself through translation. This is the geometrical underpinning of the 'fractile' [1]. The fractal subdivision results in variable density of tiles and lines at different locations across the tiling pattern. When the pattern is wound onto the spiral walls, the result is different densities at different locations in the building.
By having the unfolded building slide over the fractal tiling pattern, Libeskind was able to choose where these areas of greater density should occur. Finally, how should the graphical representation of the fractal be translated to the fabrication of the physical tiling itself? It was not practical to use different sizes.
The answer was to raise the tiles in a relief, in which the varying depths represented the different scales in the fractal [1].
The model, showing the fractal tiling that divides the facade in relief [1] 3. Sustainability and fractal architecture The idea of buildings in harmony with nature can be traced back to ancient Egyptians, China, Greeks and Romans.
At the beginning of 21st century, the increasing concerns on sustainability oriented on buildings have added new challenges in building architecture design and called for new design responses. As the language of nature, it is, therefore, natural to assume that fractal geometry could play a role in developing new forms of design of sustainable architecture and buildings [6].
Complexity can be said as an integral part of aesthetics and it reflects the surrounding place, and aesthetics again being a part of cultural dynamics. Main aim in a sustainable design should be a disease free and a healthy society through thoughtful activities treating each place as an integrated whole.
Talking about Fractal geometry it is observed that each formation is new and amazing only because fractals are like natural objects that are universally beautiful. Similarly, it is necessary that an architecture should be able to extract the essence of fractal geometry which encourages adapting to the context and time. Reality is a unity that has infinite variety 2. Harmony between wholes and parts is possible and desirable.
Fractal geometry is based on hierarchical principle, which is an essential element of urban Planning. When the geometric pattern of the spatial system is achieved with accessibility and piling which means that every space is connected to each other as well as itself it can be considered as a fractal structure [4].
Conclusion Fractals have not gained much importance outside the academic environment. May be the limited resources of architectural practice could be a reason. For long architecture has been dwelling on simple mathematics in arriving at its analytical and proportioning tools ex. The inherent repression towards mathematics by most architects has rarely allowed the designer to venture into the complexities of Mathematics.
This paper has illustratively reviewed the fundamental concepts and properties of fractal geometry theory essential to architecture design, as well as the current state of its applications. Fractal geometry has important implications for buildings. The representative review shows that architecture design is not made to be isolated but to anticipate changes in the environment.
Accumulation of technological modernizations, destroying, adapting and many changes have caused the design temporal and spatial diversity and complexity. More specifically, sustainable development in a building can be looked upon as adaptability and flexibility over time when it comes to responding to changing environments. Changing perspectives in geometric framework is mandatory for a shift from industrial culture to one that aims at sustainable designs.
The knowledge of Fractals has far-reaching impacts. In this context, fractal geometry theory offers an alternative for sustainable architectural design. This paper provides a bridge between architectural and fractal geometry theory. Thus, the 'same' or the 'regular' part of the fractal definition suggests that patterns, rules, and knowledge all repeat, at all scales: this part is sustainable or constant.
References 1. Burry, J. Sala, N. PDF 3. Lorenz, W. Parashar, R. Accessed: Lu, X. Kitchley, J. Gonze, D. Alik, B. Nile course and land formation, Aswan, Egypt, as a manifestation of fractal March Fractal geometry characteristics The core of fractal concept is the further layers of details that are displayed when the fractal structure is observed closely.
The smaller elements of the structure have the same properties as the original whole structure. Self-similarity, scaling and never-ending characterize the fractal structure and fractal concepts. The parts of a structure that is self-similar are characterized to resemble the whole structure, no matter how small the parts are Ots, In figures 3 and 4 , scaling was used to generate a natural fern and Koch curve by number of iterations.
Never-ending is one of the fractal structure characteristics which is more theoretical than practical. In natural fractal structures such as ferns, never-ending has to end somewhere, even in computer generated fractals, feedback loops have to end at a certain time otherwise the computer program crashes. Figure 3: computer generated fern. Figure 4: Koch curve.
Bovill, , pp. He introduced the idea that aesthetic simplicity which is satisfaction to the mind occurs by inner complexity. With the emergence of complexity theory general tastes and aspects of sensitivity had changed, as well the architectural consideration of goodness. Notions of self-organization systems, non-linear sciences, chaos, fractals and big bang have contradicted the simpler ones: the Newtonian linear systems. The complexity sciences have made available rules for architects, instead of creating messy complexity.
What venturi was aiming for in architecture was actually found in the characteristics of fractal. Venturi introduced the idea of using conventional parts and putting them together in unconventional ways to create a new meaning within the whole Venturi, This method of organizing parts has the potential to create a new and complex meaningful architecture. House 11a was Eisenmans appropriation of the concept of fractal scaling.
The attempted design for Venice housing competition by Eisenman was following three concepts: discontinuity, recursivity and self-similarity Ostwald, Peter Eisenman used the L shape which is originally a square divided to four equally reduced in size squares, and one square was subtracted.
These fragments are moving toward completion, which Eisenman described to be unstable and in- between figure 5 Ostwald, The scale-less form designed by Eisenman made the object to be produced at whatever scale desired. The form of house 11a can be produced to infinite scaled models, which makes it self-similar component.
Figure 5: House 11a mockup, Peter Eisenman. Efrie, , Schizo, On Cannaregio town square in Venice, Eisenman has imposed an arbitrary grid and different instances of house 11a were installed where intersections of the grid coincide with opens paces in the town square figure 6 Frampton, Other versions were placed inside the house.
Peter Eisenman published a number of works afterward; Moving Arrows, Eros and other Errors in figure 7. It was a benchmark for the development of complexity science in architecture Ostwald, This project employed scaling discourse, which depends on discontinuity, recursivity and self-similarity Hays, The terminology used by Eisenman and architectural critics to describe his work in Moving Arrows and House 11a are reminiscent of the fractal characteristics and concepts.
The iconic design of the civic center made it distinctly differentiated from other buildings located on the square Figure 8. The standardized paneled design and variation of materials made it necessarily to use an industrial prefabricated construction method.
Figure 8: Federation square, Figure 9: Federation square atrium Australia. The deep space of the extruded structure of the atrium acts as a thermal chimney. The atrium space itself is conditioned by a passive-cooling system LAB-architecture-studio, The thermal chimney works to evacuate the space of hot air and heat gained form the sun and Figure Federation square atrium, environmental analysis adjoining zones.
The fractal envelope was designed three dimensional to be used in the environmental solution. Yet the fractal geometry was used as a motif on the extruded structure. Similar to Federation square envelope, The Grand Egyptian museum winning project by Heneghan Peng architects is designed with number of mega-frames which are composed of decreasing fractured similar components figure Sierpinski gasket was founded by Waclaw Sierpinski in It is generated by equilateral triangle which recursively subdivided to its instances by number of iterations figure Figure Grand Egyptian museum.
The fractile covers all the length of the spiral wall, not only covering the building but adds a kind of mobility that keeps the building un-finished and always evolving as Balmond described. The pattern within pattern makes a structure for the other scaled down tiles. The algorithm used generates a fractal pattern with fractal dimension2 1. This non-integer dimension laid between 1 the dimension of the straight line and2 the dimension of a closed bounded area.
It shows how quickly the structure transforms from one dimension to another, from line to plane. The texture of the fractal structure increases with the increase of its fractal dimension Bovill, Ivory ceramic was chosen to cover the spiral. Tiles vary in depth to be differentiated on different scales. This method helped to prototype the tiles which is more sufficient economically and in the building construction.
Through Burry, , p. Discussion and conclusion Concepts of emergence, self-organization, evolution and cosmo-genesis rejected the concepts of determination, mechanism, reductivism and materialism. He refused the plainer, clean, white architecture of modernism, instead; his ideas were directed to the indirect architectural meanings, forms and compositions which satisfy the mind.
Complexity makes one think of how things are put together; it takes time to be perceived and decoded. Modernism perception of ornament is a crime was changed for the sake of nature.
Adolf Loos thoughts of ornaments as expensive decoration and it is a crime for the economy, waste of raw material and men power. These thoughts were rejected and post-modernists returned to think- nature.
They agreed that nature is the regulator morphology of the universe patterns. Nature is the source of patterns and the most complex ones. With the use of computer, architects tend to create computer-generated ornaments and organizational patterns. Designs became much more complex and in shape of cellular ornaments. Architects interest was directed to create designs like growing elements, and structures like crystals or galaxies.
They thought to create cellular self-generating growing ornaments that generate the whole building. Eisenman used fractal characteristics of scaling, and his project was successful in showing it on various dimensions, in the articulation of masses and spaces.
Architects depended on fractal geometry aesthetically which can be perceived by users and public. The use of fractal in architectural has not yet appeared nor has been used in morphology, masses and spaces.
Although in these two examples the facades plays a role in the architecture, fractal geometry is still fixed on the wall. As presented in examples, the use of fractal geometry became in designing of mega-panels which consist of sub-panels which contains elements that have the same shape. This prototyping makes it easily in fabrication, cost and assembling. Which overturns Adolf Loos argument that ornament is waste of money, time and men-power.
The use of fractal geometry in architecture and skin design became more economically efficient method because of prototyping. References Balmond, C. Munich: prestel. Baranger, M. Bovill, C. Fractal Geometry in Architecture and Design. Boston: Birkhaus- er. Burry, J.
0コメント