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It can be assumed that since the second half of the 20th century, landscape design has been influenced by contemporary science (DusanStupar 2001).Landscape as our living environment contains numberless elements that have crucial influences to the development of our daily life. More specifically, it includes architecture, ecology, psychology and aesthetics, etc. However, the variety current natural and cultural landscapes are continuously changing. For instance, the natural environment is regularly changing due to the influences of human activities and other nature evolution. Increasingly problems and conflicts such as pollution and soil erosion are taking place in the natural landscapes because of the development of science and industry. Secondly, the significances of new technology and science are imperceptibly influencing our mode of life, which directly leads to the different requirements of city functional structure and plan. Thus, an understanding about influence of contemporary science to landscape design is somehow necessary. This dissertation will firstly focus on describing and discussing about complexity science in contemporary landscape design using fractal design as a prime example. After that, fractal landscape design will be researched and discussed as a typical and significant complexity design method in contemporary landscape architecture. Then, a deep research about the fractal characteristic in Barcelona Botanical Gardens will be done in order to demonstrate the influence of fractal geometry in landscape design process. Finally, there will be a further discussion about the utilities of fractal geometry in landscape design in urban environments.
3 Contemporary science and fractal geometry in landscape design
3.1 Thoughts of contemporary science and landscape design
Landscape architect began to think critically about the development of thoughts in landscape design development (Dusan Stupar 2001). As a mainly accepted thought of architecture and landscape design, modernism tended to show up some problems to culture, nature and urban development. First of all, the driving force of modernism landscape architecture is industry which emphasizes the influence of human activity to the nature. Therefore, nature had been interrupted deeply during that period. The balance of space and resources between human, animals and plants lost regularly. Secondly, the traditional religions in modernism landscape architecture emphasize constancy and predictability, which means the city was planned to be a well running machine with the function of living. However, this function of landscape and architecture in this thought could be repetitive and lack of vitality. Lastly, the design language of modernism landscape shows mainly Euclidean geometry which comes from the ideal geometrical form such as round and triangle. It has some aesthetic characteristics but cannot fully demonstrate the beautiful of real nature. In the meanwhile, as has been talked above, the influence of new technology and contemporary science provided people new view of nature and the whole universe. People realized that our world was more complex and had more dimensions which are changing and flowing forever. In addition, the elements in this complex world are affecting each other and the whole nonlinearly. The cosmos is much more dynamic than either a pre-designed world or a dead machine (Jenkcs 1997).Contrasted with modernism design theory, the 'science of complexity' explores a more creative world, which influenced contemporary landscape architecture design deeply as the main principle of post-modern design.
3.2Relationship with Complexity science and landscape design
Complex theory took off with the advent and development of computer which can shoulder the huge number of data arithmetic related to the complex phenomenon of nature and city plan. It mainly concerned with self-organizing phenomenon and the effect of one sub-system's variation on another and the whole. Thus, it can be used to research Biology, Sociology, and Psychology and all the subjects that have crucial influences to Landscape Architecture.
As a significant science theory, complex science influenced the studies and design process of natural biology, aesthetics and city plan. More specifically, it has great significance in the in programming, site analysis and interpretation, form grammars, and even construction techniques. In the area of biology, the research of both dynamic and static relationship between animal, plants and nature environment can help designers focus on timeless change in ecological phenomenon with scale during the whole process of nature landscape research and design. When it comes to urban plan, economy and social culture contribute a lot to the spatial form of city. Scientific research about them in different scales has important significance to the city development and people's daily life. overall, compared with traditional design theory, complex science demonstrate on a more active environment with continuous changing components, which is a distinction from traditional modernism and leading designers to have a more open, dynamic and surprising viewpoint of landscape architecture.
As a science discovered from nature and universe, complex science includes fractals, chaos, folding, bifurcation and many other theories. Evolution, emergence, self-organizing, adaptive and self-similarity is their common feature. In this dissertation, fractal and its influence to landscape design will be described and discussed as the major content by reason that fractal demonstrates the law of both nature landscape patterns and distributions of different elements( e.g. animals and plants, people and environments). Moreover, as a language of nature, fractal geometry could describe the self-similarity characteristic that belongs to most natural elements in different scales, which is important as 'ecological aesthetics' in landscape form generation. The principle of fractal geometry and its materialization in landscape could improve both the aesthetic value and ecological relevance of the designed landscape.
3.3Introduction of fractal geometry
'Fractal geometry will make you see everything differently.' (Barnsley, 1988)
Fractal geometry is a new science and mathematics theory exploring both irregularity and equilibrium of nature, which has been accepted and used in many areas. Benoit Mandelbrot was the first who systematically summarized the self-similar phenomenon in nature using mathematics ways and named it fractal geometry (Mandelbrot, 1977). He wrote that many natural forms and processes had a common characteristic which was named self-similarity. More specifically, they displayed the similar shape in different scales, which was also known as scale-invariance. For instance, when the coastline on the satellite view was zoomed randomly to a larger scale, the shape of the topical line was similar with the whole. Moreover, similar phenomenon existed in the process of changing nature system, including the interaction between eco-system and activity of animals. The concept of 'fractal dimension' was used to measure and describe the natural patterns. The forms and spaces at one scale were measured and observed first, and then those at other features of scales could be described by the ratio transition. Comparing with integer dimension of traditional Euclidean geometry, fractal geometry has a kind of so-called 'fractal dimension' which has a value between one, two and three. Thus, as a geometry belonging to complex science, fractal geometry has the characteristic that more efficiently shows the complexity and laws of nature. That makes it more suitable in describing and reflects the sense of nature in both intuitionist and abstract way during the landscape design process. Thus, compared with mathematicians who focus on the mathematic theory, landscape architecture and artists tend to specialize on the symbolic meaning of fractal forms and the connotations of spatial, temporal and other areas related to fractal and nature.
(PIC)FRACTAL COASTLINEfractal coastline.jpg
As we all know, traditional geometry is always described as 'cold' and 'dry'. The major reason is that it could not describe the form of elements in nature such as the texture of earth, could mountain and even a tree. Compared with that, fractal geometry entirely described the characteristic of nature. Fractals are irregular shapes whose geometry is scale-dependent (M. Batty&P. Longley, 1986). More specifically, at every scale in a whole in nature, every single part appears the similar form characteristics with the whole and each other, which is so-called self-similarity. This theory is existing in most of the natural forms and processes and efficiently demonstrates the complexity of nature, thus it could be greatly helpful to create a new aesthetic in landscape design (Baird 2002&Spirn1988).
4 literature reviewï¼šThe aesthetics and ecological value of fractal geometry in landscape design
4.1 The aesthetics value of fractal geometry in landscape design
As is known to many designers and psychologists, aesthetics plays a key role in how we perceive the environment around us (Nassauer, 2002; Tuan, 1974). As a result, during the last few decades, people started to aware the importance of aesthetics in natural landscape which shows the relationship between us and the non-human landscape. Moreover, an aesthetically designed landscape could also enhance people's awareness of nature protection and ecologically sustainable development.
4.11 ecological aesthetics and landscape
Thousands of tears ago, Greek scholars regarded art, aesthetics and beauty as important subjects in philosophy. They insisted that sense of beauty and other visual phenomena plays a key role in people's emotion experience. The conception of these theories had been greatly developed and enriched during the eighteenth century. For instance, Immanuel Kant (1724-1804) had a deep research of the purpose, significance and mode of action of human psych motility, including people's estheticism and fantasy in his third critique, the Critique of Judgment, Which is believed to be the first philosophical system to explain aesthetics theory and have great significance even in current society. However, it was Alexander Baumgarten (1714 - 1762), a German philosopher, who started to research systematically about connecting conscious and sensory experiences with emotion generation, which is called 'sensory cognition' (Goldman. 2001).He insisted that aesthetics is a way of 'knowing'. Moreover, he divided the concept of aesthetics into two parts which is 'sublime' and 'beauty' using the sense of people in environments from large to small scales.
This theory developed a lot during the early 20th century. In the areas of landscape design, the understanding of environmental aesthetics had been greatly enhanced and people started to realize the relationship between aesthetics, ecology and their impact of human emotion. However, the complexity of the images and textures in nature was far beyond the traditional landscape architecture to describe it. Moreover, the design method in traditional design for form creation such as contrasting, emphasizing and balancing could not efficiently reflect the basis complex principle of nature, especially in all different scales. Thus, it was also difficult for them to explore an ecological and sustainable landscape with natural and ecological aesthetics with advisable spaces and patterns.
4.12 fractal geometry as language of nature
Based on what has been discussed above, one of the most important principles in landscape architecture is to find out the potential space form and patterns that could demonstrate the image and process of nature systems with ecological aesthetics. It is obvious that natural form has been inspiration for art, architecture and landscape design throughout the design history. However, as has been discussed above, traditional design method tended to show the limit in describing the characteristic of nature and not until the last several decades did designers realize that many nature forms and patterns has their own characteristic such as fractal geometry, which has both science and aesthetics value(Mandelbrot, 1977). As a result, fractal geometry could be a special and visual language for landscape design to articulate the complex forms and patterns in nature (Thayer, 1989).
Many examples demonstrating the fractal character could be found in the environment where we are living. For instance, when the image of texture on a tree bark is zoomed to different levels of magnification, the fractal self-similarity appears in the edge lines and fragmentary surfaces. Although the patterns are not geometrically identical and the range of fractal character is limited by the whole size of tree, the existence of fractal geometry in nature can be proved and put into practice for reference in organizing the spaces and patterns during landscape design.
(PIC)TREE BARK AT DIFFERENT LEVELS OF ZOOMING INC:\Documents and Settings\Administrator\æ¡Œé¢\dissertation\pic\tree bark1.jpg
4.13 fractal geometry in landscape design
As a matter of fact, before the creation of 'fractal' concept, designers had unconsciously used the pattern and forms with fractal characteristic as an important aesthetics reference in some designed landscapes. For instance, the research of the dry landscape garden of Ryoanjii Templein in Japan has showed several fractal patterns in the main landscape structure (Tonder & Lyons 2005). Ancient designers used a technique which is called medial-axis transformation to change the number and places of the rocks and moss within the dry garden. Connecting with the building, it is found that a special form with a visual principle which is similar to a branching tree appears in the overall landscape structure. The position and form of rocks, moss, arranged gravel and the plan of building formed an abstract self-similar form of tree which is moved topologically near the medial axis of each 'branch'. Thus, it is proved that the appearance of fractal characteristic in the former landscape design was not accidental but based on a junior understanding of the fractal patterns in nature. Moreover, fractal geometry could be a potential connection linking landscape aesthetics to the nature.
(PIC)Ryoanjii Templedry landscape garden of Ryoanjii Temple.JPG
In order to have a more specific understanding of the fractal dimension and characteristic of both designed and natural landscape, a scientific analysis was taken by Stephen Perry and his partners. They took pictures of several places from different view point. Each group of photographs was taken at different times. All those places range from natural landscape to typical urban landscape. Then, every photograph was turned into 8 bit grey-scale image. After that, the pixels in all rows and columns of each image in different colors were recorded and the results were transformed into frequency signals. Based on that, 1-dimensional fractal for each row and column was obtained after all the frequency signals were plotted in a line chart. Finally the 2-dimensiondata was obtained by adding 1 on the 1-dimension figures (S. Perry, R. Reeves & J. Sim, 2008). After the research, they obtained a conclusion that fractal dimensions of highly urbanized landscapes tended to be lower than those of natural landscapes (S. Perry, R. Reeves & J. Sim, 2008).This research proved that it is possible to use fractal geometry to access the degree of naturalness and urbanization in certain spaces although the research method may need more advances. Moreover, other researchers showed that advisable fractal form and dimension could influence people's preference for the designed landscape. Surveys also demonstrated that people preferred naturalized landscape based on fractal property, comparing with a purely rigid geometry property (Tanja Simonic, 2003. Purcell, 2001).
As has been talked above, fractal geometry is a language from the nature and could be an initial basis in landscape patterns. It is potential to be the generation of landscape forms and patterns that have natural sensuousness. Moreover, these visual and other sensuous effects could be factors in identifying the ecological diversity, function and sustainability. Thus, it is possible that the fractal characteristic of a designed landscape could affect people's sensibility and emotion. However, unlike an image of an individual natural surface, landscape design is extremely complex, involving both natural and man-made constructions. In terms of a designed landscape, the viewpoint should not be single but changing and moving as time goes on. Moreover, detailed research about the environmental factor should be taken to have an entire concept of the fractal character of the sites. Besides that, an understanding about utility of fractal geometry in analyzing the relationship between landscape patterns and different species of animals and plants is also necessary during the landscape design process, which will be described and discussed in the following paragraphs.
4.2 Influence of fractal geometry to eco-system.
It is assumed that fractal geometry plays a key role in the aesthetic aspect in both natural landscape design and other type of landscape containing natural characteristics. As well as that, as a science coming from nature, fractal geometry could be used as reference to control and enhance the ecological balance by dynamically affecting the elements of landscape patterns such as climate, distribution of plants, animals and water, etc. Compared with the aesthetic value, this influence in ecological system is, in a certain sense, a more dynamic interaction between landscape patterns and different natural species. More specifically, the ecological design based on fractal design with the help of computer efficiently focuses on the fractal character of natural landscape which is timelessly changing. In addition, it has made a great contribution to the research of the relationship of the natural sites, plants and animal behaviors in various scales (B.t.Milne, 1990).
There is no doubt that the distribution of plants, animals and other natural element s such as rocks, water and earth could gradually influence the whole ecological system. For instance, when the number of snakes reduced due to the excessive and indiscriminate hunting by people, the quantity of field mouse would increase rapidly. This would be a threat to both natural plants and crops. As a result, the percentage of each natural element would have great changes, which would also change the overall landscape structure. On the other hand, the landscape structure and patterns influences the distribution of different species, the territory and migration of animals and other dynamical landscape elements. The interactions discussed above range from a short-lived change such as the migration of bird in one year to a long-term process in millions of years (Delcourt H.R., 1983).In addition, the spatial extent varies from a square centimeter to the whole earth. Thus, the nature landscape is always in change due to numberless intricate factors in various processes at different scales of time and spaces.
Based on the discussions above, animals and plants in nature interact within a certain landscape at various scales (Woodward, 1987). Different species of animals influence their environment by their movements and actions with different purposes. Furthermore, the spatial and temporal scales of animals in various scales could be summarized and measured with the help of computer and measuring facilities. More specifically, a landscape pattern, designed or natural, could be comprehended by the rich and colorful species researching about the scales at which they active in the landscape (Morse et al., 1985). In other words, the relationship of organism's activity at different scales of time and space could be adopted to determine whether a landscape's pattern and scale is harmonious with the organism living within it. Generally, a naturalize landscape system has a long-lived period of development in which the elements within it (e. g. animals, plants & water) kept on interacting with each other. As a result, compared with artificial landscapes, natural landscape usually has a more stable and appropriate spatial for organisms. Special managements such as weed cutting and energy supplying are mostly necessary in man-made landscape for keeping the landscape patterns and eco-system runs as they are supposed to. One significant cause of this is that appropriate spatial scale and pattern for both moving and still organisms has been generated in the natural landscape during a long complex course of events, which most man-made landscape lack of.
The spatial scales of natural elements are so complex and mutative that they could hardly be measured and predicted. However, in the principle of fractal geometry, all the elements at any scale in nature could be regarded as parameter which is not only similar to the whole but also able to influence the whole system and the process. This relativity may be both static and dynamic. In another words, fractal geometry demonstrates the character of the complex natural process. Thus, an appropriate naturalized scaled landscape based on fractal geometry has long-term benefits to eco-system and the subsistence of living creatures. As a result, designers could integrate the fractal dimension with the scale of coverage with density of plant, animal home range and other natural elements (Mandelbrot, 1983), which may be greatly helpful to explore and create naturalize landscape design language in landscape survey and design. As a matter of fact, many landscape patterns of existing natural landscapes could be great example of how fractal character operates in the interaction of natural elements. For instance, proportioned fractal scales and patterns are found from the analysis of the Amazon Forest. It can be observed that obvious fractal patterns appear on the satellite map of this historical natural space. Besides, fractal patterns between forest and Amazon River and that in the wetland with the river in certain scale containing different elements have shown distinct characteristics and fractal dimensions. One of the most important causes for this is that there are different natural elements included in these spaces. Moreover, the distinct fractal pattern implies the distribution of plants and the various home ranges of animals in different body mass and habit, which also conversely influence the fractal landscape patterns (Milne et al., 1991). By contrast, those parts which have been disturbed seriously, a great deal of factors resulted in the faint and degeneration of fractal character in the plan view, which is a process with time fluctuation. The result of contrast suggests that it is possible to create a naturalize landscape which simulates the configurations of animals, plants and other natural element with the help of fractal patterns summarized from appropriate examples. In addition, the quantities of density and coverage rate of patch areas in these two images in different time could be calculated by the general fractal relation: Q(L) =kLD, in which Q(L) stands for the quantity, L means a length scale, k is a constant and D is the fractal dimension (Mandelbrot, 1983).
(PIC)AMAZON FOREST C:\Documents and Settings\Administrator\æ¡Œé¢\dissertation\pic\Amazon Rainforest.jpg
During the last decades, landscape architects have began to dabble in the attempt at putting fractal geometry into practice during the landscape design process, either in establishing ecological systems or creating visual and spatial effects. Bet Figueras, a Spanish landscape architect, had a meaningful research of adopting fractal geometry as an important principle in her Barcelona Botanical Gardens design, which will be described and discussed in the next paragraphs.
5 Case Study: Fractal design in Barcelona botanical garden
5.1 Context of the Barcelona botanical garden project
The project of Barcelona botanical garden was situated on Montjuic in Barcelona, which used to be a part of the unused spaces between the seaport and Barcelona city. Montjuic Mountain is a small hill with a height of 200 meters in the south of Barcelona. It used to be a crucial defensive centre and the defense castle was reconstructed as a military museum. During the last decades, a great deal of important issue such as the Olympic Games (1992) and World Expo (1929) took places in Barcelona city, which leaves many important urbanized landscape and architectures in this area. However, large pieces of natural space covered by various plants are well preserved during the recent years, which play a key role in the microclimate and the urban inhabitants' daily lives. The physical and cultural environment of this area demonstrated typical Mediterranean character which is made up by the relaxed rhythm of life, dry earth and irregular patterns in landscapes and city plan.
The site of Barcelona Botanical Garden was carefully chosen on the south-western versant of Montjuic Mountain. This location is highly above the whole city, which could endow with a wonderful view across the whole city and the delta region landscape of the Llobregat River. Besides that, the site of design is also an important connection between the urban architecture community and natural unused areas. The local authority held an international competition of building a new botanical garden in the 14-hectare land opposite the Olympic Stadium. The scheme put forward in the competition is to design a new botanical garden which was proposed to show the abundant plants from the countries that mainly has Mediterranean climates with a new landscape design language. That proposal of project put forward a high request in various areas of subjects such as art, botany, geography and so on, which is obviously a challenge to the designers related to complex science. In addition, designers also had to deal with the rugged topography on the mountain and the subtle relationship between the site and the local cultural environment.
5.2 Fractal characteristic in the landscape form generation
Bet Figueras and her company won this competition in 1997 with their modern landscape design language. As a start of this project, they put forward two general issues to consider about. The first consideration is to find out a new landscape form that could intervene and interact well with the topography and cultural environment. Then, they were willing to create new garden structure which could fully demonstrate the Mediterranean plant communities from countries around the Mediterranean sea and those areas in the similar latitudes such as California, the northern part of Japan, South Africa and Australia (Figueras, Ferrater & Canosa, 2006).
Based on the initial considerations of this project, B. Figueras used fractal geometry as the basic concept at the beginning of design. After a detailed research of the natural and cultural environment of Montjuic, she put forward a triangular network as the original language over the bumpy terrain. Then the apexes and aspects grid was adjusted according to the three dimension scale of the mountain surface, which made up the initial concept of landscape form. After the design team created the three precise dimensional model for the topography of Montjuic which could also be regarded as 'fractal islands' (Figueras, et al, 2006), the initial three dimensional grid was projected onto the fractal island. As a result, the grid could be relevantly manipulated by the topography of the site. Subsequently, the vertical parts of the apexes on the grid were adjusted to follow the main direction of each slope. At the meantime, the space with different functions such as plants areas, paths and water features were roughly presupposed according to different characters of generated spaces by the computer on the grid. Generally, Figueras and her team put forward some important issues that the modification of the fragmental geometrical shapes should make allowances for several basic demands according to the principle of project. For instance, the base installation such as drainage network should be hidden in the lower space in the whole grid system. Moreover, there should be a plan for the hierarchy of the slopes in scale and area according to different functions. Eventually, the aspect of position and scale of buildings which has certain functions should be considered and marked out in anticipation (Figueras, et al, 2006). After the process of form generation with the help of computer, the original conceptual master plan with elevations was created. Certain triangles in the design would be subdivided into smaller part and topologically modified to adopt more detailed functions or micro-perspective features.
The main aim of this design that Bet Figueras mentioned in her statement was to demonstrated the development and character of Mediterranean landscape, in addition, they were willing to have a new attempt to explore the landscape form based on the long-range development of the local species and husbandry. To some degrees, the work of concept and landscape form generation successfully explored the main ideas of the project. First of all, it can be seen from the comparison picture that the landscape pattern are very similar with pattern of the whole city plan which has a long-term history. More specifically, the landscape pattern in Barcelona Botanical Garden is, in some sense, an extension of the texture of the whole city in a smaller scale, which conformed well to the principle to fractal geometry. As a result, compared with the scale in which people drive and take trams in the city, the generated pattern could support a pattern at a more humanly scale which in the meanwhile relates to the basic pattern of the city for walking and riding. Moreover, triangles could be utilized to form the spatial connection and topographies easily in fractal landscapes due to its mathematical characteristic. As a typical post-modern aesthetic, this language has appeared in many artists' works. One of the most famous artworks is the abstract painting named 'Mediterranean' created by Pablo Ruiz Picasso. The triangles which play a key role in the visual effects in the painting make up the roads, grass, farmlands meadows and construction elements. All of what has been talked above has proved that triangle is suitable for this fractal landscape design in the sense of aesthetic. Secondly, in terms of design language, fractal geometry as the design language of Botanical garden fits well with the proposal and aim of this project. It demonstrated the natural idiom of fragment and irregularity in both grand and human scales in a modern design language. In the meanwhile, the loose triangular net-work in the walking and rest areas could provide visitors a relaxing and active sense. Because of the fractal principle of the spatial plan, the roads and paths are no longer linear spaces, instead of that, all the functional areas in the garden are treated as spaces in different scale levels. As a result, spaces of paths, water features, some planting areas and relaxing spaces are merged, which support users a relaxing but clear touring environment. Finally, it fits well with the cultural style in Mediterranean area to use triangle as the basic shape in the fractal landscape. More specifically, triangle and other linear types which are made up by triangles such as rhombuses are regarded as different species of animals in Mediterranean traditional culture. Thus, these kinds of shapes are well accepted by local people and could also provide the visitors the abstract impression of the local culture and arts.
Interestingly, similar form concepts appeared in another landscape design and plan research. Several years later, there was a research of how to organize the unused space in the area of Montjuic. Ferrater, a Spanish designer who is from the same company with Figueras took the project. She linked the unused areas in irregular and discontinuous shapes according to different topography and planting coverage to create the connection between the unused areas and the surrounding functional areas and, in the meanwhile, create a new system of communication and access (Ferrater, et al, 2002). She merged the topography and wood in both vertical and horizontal dimensions. Moreover, she connected the wood areas, potential useful areas and the main routes on the general map. Finally and coincidently, she got a visual plan in which different areas were organized topologically in triangular shapes as geometrical units and the whole master plan had a similar vision as the plan of Barcelona Botanical Garden although they were at different scales and designed in different periods. It could be surmised that triangle is well accepted by Spanish landscape architects in landscape design and plan to explore the landscape of Barcelona as a basic geometrical unit.
5.3 Fractal geometry in the planting design and plan
The design team insisted that the clarity of landscape structure in the garden was determined by not only the basic geometry structure but also the layout of vegetations. Besides that, one of the most important differences between botanical garden and other functional green spaces is that botanical gardens not only contain various plants but also exhibit them with the theories of ecology, taxonomy and aesthetics, etc. Thus planting design was treated as initial work as well as spatial landscape design. As a modern botanical garden, Barcelona Botanical Garden has a clear and ingenious planting layout as well as its post-modernism landscape design. In the meanwhile, fractal geometry exists in the plan of different kinds of plants as the rule of nature.
There are no less than five independent areas in the world which has typical Mediterranean including Mediterranean basin, California, Chile, South Africa and part of Australia. There are a huge number of plants in various species and scales from these areas. The design group organized the vegetation according to the relationship of geography and ecological sibship and established eight main Exhibition Areas. In this process, the design group attempted to simulate the fractal dimension of nature instead of used fractal geometry to create an ultra-artificial appearance of the planting area (Figueras, et al, 2006). In particular, they arranged the plants from different areas according to their size and species and put the vegetations which have the similar competitive strength near to each other. Based on ensuring the geometrical and ecological location of each species, the plants in the garden was assigned arrayed roughly in radiate layout. In more specific terms, low scaled vegetations such as groundcover are near the center of each area and high trees and shrubs are located close to the edges. While most mesoscale plants are between the two types above. This provides visitors a stratified and organized visual system during walking. In the meanwhile, fragmentized spaces merge the individual exhibition areas into each other spatially while the routes go circuitously between them.
From Aquatic plants to land plants and wild woods, 72 plant communities are located in one garden and utilized as a colorful palette by the designers. Plants as natural elements were not artificially treated such as being cut into geometrical shapes or arranged in awkward patterns. Instead of that, it could be seen from the vegetation analysis plan that they are connected as an ecological network and an integrated system although they are from different areas all over the world. Thus, the planting design in Barcelona Botanical Garden follows the fractal dimensions of both individual vegetation and plant communities in scales, species and locations. As a result, the process of nature is reflected by the natural communities imitated by the plants and would provide the organisms a wild and naturalize environment to grow within and, in the meanwhile, keep the distinguishing local characteristic.
5.4 Final Discussion
As has been discussed above, generally, Barcelona Botanical Garden is absolutely a creative attempt during the history in landscape design method. The concept of design is infiltrated into all the parts of this project. It can be observed in the gardens that even the treatment of the retaining walls and benches conform to the form concept of fractal triangles. Bet Figueras, the designer and design team member, called it 'a botanical garden full of plants and fractal atmosphere', which expressed that fractal geometry as a typical contemporary complexity science runs as a crucial rule through the process of design in the terms of both aesthetics and ecologic. There used to be several difficulties and challenging during the design process, for example, it was a problem of the design about the 'gap' between the garden and surrounding environments including grass and functional constructions on the mountain. However, the design team solved this problem by using the planting strategy which has been mentioned in the former paragraphs. Specifically, they planted the larger trees and shrubs near to the edge of each exhibition area, so the edge line was weakened by these 'soft landscapes', which efficiently solved the problem above while expressing the planting concept at the same time. It should be admitted that there are several problems and shortcomings that needs to be improved. For instance, the maintenance of landscape construction in the garden tends to show up some problems such as slight damages on the concrete paving for the reason that there is a great deal of extensive exposed concrete lab due to the modern design concept which creates a great deal of large area spaces within the routing spaces. Despite this, it offered great contribution to the research process of new form in landscape design and provide people fresh way of thinking of our world. Moreover, fractal geometry in the design process became one of the most important components of parametric design which is regarded to play a crucial role in our future design.
Both the literature review and case study have presented that fractal geometry as an important complex science contribute a lot in contemporary landscape design theory. More specifically, it provides us new angles of view about the formulation of both the whole world and subtle elements surrounding us, which has a great deal of influences to the thread and process of design. The process of landscape design was transformed from form illation to form generation which starts and goes with complex factors that influence landscape through various dimensions. The complex science offers landscape new opportunities of patterns which could adapt to the whole natural systems and eternal changes.
Besides what is discussed above, the principle fractal geometry has been utilized in modern city plan. Our current city is gradually showing up its unintentional complex tendency compared with the environment we lived in long time ago due to the development of contemporary science. In the meanwhile, traditional theories of technology, culture and people's behavior have been challenged. In more specific terms, as has been mentioned at the beginning, the science in nowadays has greatly changed our social and cultural environment. There are increasingly more components which make up and influence the city structures and patterns. The functional spaces such as subways and vertical gardens which are created by the recent technology have greatly extended spatially and culturally which can been seen on the comparison charts of city master plans in different years. However, the new sciences of complexity such as fractal are showing their advantage and adaptive faculty in our modern society due to their new understanding of world. In particular, the original pattern and development of city plan could be summarized with the help of fractal geometry because the growth of patterns has substantial similarities which are relevant to the growth of nature. Based on that, it is possible to plan and predict the further patterns of a city through utilizing the elements such as traffic lines, river lines and coverage of recourses as the regulation of parameters to control the complex city systems. In respect of the human scale, fractal geometry could help to assess a functional area if its scale and patterns are harmonious with the physical and social environment and residents' behaviors.
Above all, landscape design as well as other design areas is having a notable progress as time goes by. Designers tend to think more frequently about the tendency of design method and thread. Increasingly more questions such like 'how will our future landscape look like' are mentioned in the researches. However, the complexity science and has offered designers creative view of this area and new thought of how our environment is potentially developing. With the help of new digital technique and complexity theory, complexity science is playing a increasingly more important role in the landscape design history.