The contrast between the fractal pattern and the traditional textile print pattern Tang Ying1, Fang Kuanjun 1,2, Shen Lei 1
(1.Key Laboratory of Eco-Textile Ministry of Education (Jiangnan University), Wuxi 214122, China; 2. National Key Laboratory Breeding Base of New Materials and Modern Textiles, Qingdao University, Qingdao 266071, China)
Abstract: Fractal patterns and traditional textile prints belong to different aesthetic categories. By analyzing the aesthetic characteristics of fractal patterns and traditional textile prints, the aesthetics of fractal patterns and traditional textile prints were carried out in terms of symmetry and balance, singularity and harmony, repetition and gradation, rhythm and rhythm, simplicity and complexity. In contrast, it is pointed out that although the fractal pattern has its unique visual aesthetic value, it has certain limitations in printing technology, creative mode and cultural connotation. Traditional textile printing is still irreplaceable.
Key words: fractal pattern; traditional textile printing pattern; aesthetic characteristics; form beauty; inkjet printing CLC number: J 523.1 Document code: A
Article ID: 0253-9721 (2009) 12-0090-05
Fractal art is a new type of media art created based on fractal geometry theory, which is the application of computer technology in the field of graphic image art [1]. Fractal patterns have unique aesthetic characteristics. Since its birth, they have had a major impact on physics, biology, geography, and even philosophy, history, and art. In recent years, many scholars have studied the application of fractal patterns in textile print design. Li Gang et al. [2] discussed the feasibility of applying fractal graphics to textile pattern design. Yang Xuhong et al [3] used the VB language to write a program based on the composition principle of the fractal L system to generate typical fractal curves and produce various artistic patterns suitable for textiles. Zhang et al [4-6] based on the characteristics of textile fabric printing patterns, based on the generation principle of trigonometric Mandelbrot set and generalized Julia set, using IFS random iterative algorithm, a series of discussions on the methods and approaches of textile printing pattern design . The graphic generated by the fractal method has outstanding visual effects and strong decoration. It can be expressed on the fabric through digital inkjet printing technology, and it is completely feasible to convert into a printed pattern.
Traditional textile printing design belongs to the field of arts and crafts. It is influenced by many factors such as production technology, customs, consumer market and fashion. It has formed its own characteristics and has traditional artistic expression methods and aesthetic concepts. The fractal pattern shows a new artistic style, which not only has the aesthetic standards of balance, harmony and symmetry of traditional textile printing patterns, but also more than the new performance of these standards [7]. Mastering the similarities and differences between the fractal features and the traditional aesthetics of traditional textile prints can better apply fractals to textile print designs. This paper explores the artistic value of fractal patterns by analyzing the aesthetic characteristics of fractal patterns and traditional textile print patterns, as well as comparing the formal beauty of the two.
1 The aesthetic characteristics of traditional textile printing patterns 1.1 The point-and-line surface representation based on Euclidean geometry The traditional textile printing pattern is restricted by the processing technology. In the design process of pattern, color and composition, the Euclidean geometry method is usually adopted, through the application of aesthetics. Principles and composition rules, which perform stripe repetition, transformation, or cross-combination, arrangement, layout, and color change of patterns composed of basic geometric elements to produce various modeling patterns. This method based on Euclidean geometric pattern generation and design enables the drawing of more complex individual patterns or regular combination patterns composed of basic patterns, as well as irregular abstract patterns. The composition level is relatively simple, the color registration is simple, and the expression techniques are mainly flat coating, Hook line and mud point.
1.2 Symbolic and abstract generalization The origin of traditional textile print patterns is usually divided into two types: one is the natural thing, and the other is the traditional pattern [8]. The rich and colorful things in nature require designers to refine and process on the basis of sketching. After artificial abstraction, they form various patterns suitable for textile printing. The symbolic figure is the most influential and most influential figure in traditional decorative graphics. Its content involves various aspects such as flowers, plants, animals, landscapes, totems and religions. It is widely used in textile printing patterns. Figure 1 shows a typical floral print pattern. The designer extracts the characteristics of the flower elements in nature, applies the transformation of the dotted line, abstracts the shape of the flowers and stems, and reflects the depth and shade of the interlaced layout and color. Layering. 
1.3 Flatness Flatness is an important feature of traditional textile print decoration. It breaks the pattern of focus perspective, adopts moving line of sight, and observes at equal distances. The objects displayed are all looking flat, not showing the top and bottom. The planar configuration of the traditional textile print pattern discards the change of the space before and after the shape, and the shape and shape are horizontally parallel or vertically aligned, and the size is changed according to the performance content and the theme. Focus on depicting the form itself, focusing on the contour features of the form, and being good at grasping the dynamic contour features to exaggerate. The form of expression is concise, expressive and vivid, full of drama and decorative beauty.
2 Aesthetic Features of Fractal Patterns 2.1 The Beauty of Non-European Geometry Traditional textile prints are typical Euclidean geometric patterns, mainly referring to the ideal form abstracted from nature, such as triangles, circles, squares and other geometric forms. Non-Euclidean geometry is relative to Euclidean geometry, mainly refers to the aesthetics created by the fractal algorithm that are different from the general Euclidean geometry. Non-European geometry no longer treats the point-and-line faces in a separate light, but treats them as a whole. Figure 2 shows the most classic Mandelbrot set in a fractal pattern. It is generated by a simple mathematical formula, but it creates a dreamy and beautiful pattern, and any detail of it can be transformed into a more wonderful scene. 
2.2 Self-similarity Self-similarity refers to the generation of many parts or individuals similar to oneself in the generation and development of things [9]. Self-similarity is the core of fractal theory and the most basic and fundamental feature of fractal patterns [1]. The self-similarity of fractals is characterized by their morphological convergence in the relationship between the local and the whole. The beauty expressed by this convergence is the hierarchical organizational beauty produced by self-similarity in fractal beauty. As the number of fractal levels increases, the self-similarity between such adjacent levels tends to lead to a psychedelic sense. If in the textile print design, the psychedelic beauty generated by the fractal self-similarity is used to construct the interesting space between various pattern elements, the unexpected visual beauty can be achieved.
2.3 Infinite fineness The complexity of the fractal pattern comes from the iterative iteration of simple mathematical formulas, and its appeal is in the self-similarity between the infinite level local and the whole. Graphics are embedded in graphics, producing details on smaller and smaller scales, resulting in an endless array of refined structures. The infinitely fine aesthetic features of fractal patterns are not expressible by traditional textile prints. As the fractal pattern continues to refine, all hidden information and order are constantly emerging, so that people's vision is drawn by its magical infinite subdivision structure, constantly creating new artistic charm and beauty.
3 The contrast of the pattern in the form of beauty 3.1 Symmetry and balance The symmetry in the traditional textile print design is an absolute balance, is the most common aesthetic form, usually the same mass or the same pattern is equally spaced on both sides of the axis of symmetry It is a combination of the same shape and the same amount. It gives people the feeling of order and solemnity, and presents a kind of peace and quiet. The pattern of the equilibrium shape generally adopts the organization method of equal amount, special shape and different color, and sometimes adopts the method of the same shape or the different shape and the same, and maintains a plane equilibrium state in the composition structure. The fractal pattern has infinite bifurcation and entanglement. The pattern is omnipresent in its inner order, and has a self-similar structure, that is, local and overall symmetry. This symmetrical form abandons the ambiguity of the Euclidean geometric form, and the whole picture looks for dynamics from the balance. At the same time, it has a general correspondence and constraints at a deep level, reflecting a dynamic balance. This balance has greater flexibility and freedom compared to the balanced aesthetics embodied in traditional textile prints, bringing new artistic charm and beauty.
3.2 Singularity and Harmony Singularity and harmony are the relations of unity of opposites. Singularity refers to the distinctive part of the pattern, and harmony refers to the cooperation, association and consistency between the various pattern elements. The singularity of traditional textile prints is subjective and pre-conceived and drawn by the designer, mainly reflecting the freshness created by the transformation between the pattern elements. Traditional textile print patterns tend to express the overall harmonious beauty. Through artificial regulation between patterns, colors and composition, a harmonious, master-slave and balanced unity is finally formed, which makes the overall visual experience tend to be harmonious. Singularity is a kind of beauty, and singularity to the extreme is a kind of beauty [10]. The beauty of fractal is a kind of singular to the ultimate beauty. This kind of singularity is a typical chaotic beauty. It is a singularity in harmony. It is reflected in its local and overall symmetry and repetition, and the shape and color are neat and consistent. Test, giving people a sense of harmony. Compared with traditional textile prints, the fractal pattern is based on the singular expression of uncertainty and sporadic color [11], and the harmonious beauty that combines neat order and chaotic disorder, to a certain extent, It is more suitable for the development trend and trend of modern textile art, and can meet the aesthetic needs of different groups of people.
3.3 Repetition and Gradation Traditional textile printing patterns are repeated in various forms, such as scatter, corrugated, and crease, etc., which are repeatedly arranged by different combinations. The most common quadrilateral continuous pattern is to continuously design a complete flower back through the up, down, left and right stitching, or to change the position of a graphic and then appear one or more times. Fractal patterns are generated by repeated digital processing using a computer. The repetitions expressed by them are not repetitive appearances of graphics, but rather mathematical and orderly features with randomness, contingency, and even dynamic changes. Traditional textile printing patterns are limited by the printing process. In the gradual change, it is usually necessary to use a multi-level transition of the dotted line surface. The softness is slightly lacking, and the color transition performance is not natural. The fractal pattern is generated by an iterative function. After defining the mathematical model and algorithm, it will operate according to certain rules. The change of each shape in the pattern, the transition of each color is a natural flow, without sensation [7], and can be perfectly reflected by digital inkjet printing technology.
3.4 Rhythm and Rhythm Rhythm and rhythm are important factors in the form of the beauty of textile prints. The traditional textile print pattern is mainly performed by a combination of some formal factors. The common composition forms are two-way continuous and square continuous. This orderly sense of rhythm, in the repeated cycles, presents a harmonious and appealing rhythmic beauty that can evoke emotional changes in the audience.
Fractal art creation focuses on the rhythm of nature. The grasp of rhythm and rhythm in fractal patterns is the result of the combination of rationality and sensibility. The change of rhythm is related to the number of iterations, while the sense of rhythm is bred in the formula. As shown in Fig. 3 [12], with a simple primitive (a), different scale details can be generated by repeated iterations of certain rules, and patterns with completely different rhythm patterns can be obtained under different iteration times. The rhythm in the fractal pattern transcends the simple form arrangement, but changes alternately, and the rhythm brought about by each iteration is different. 
3.5 Simplification and Complexity Simplification is one of the characteristics of traditional textile print design styles. In the traditional textile print design elements, abstract, geometric element graphics occupy an important position, generally using simple patterns to be reconstructed and combined to form a visually rich complex pattern. The word "complex" is a combination of the words "complex" and "hetero". The main meaning of "complex" refers to the diversity, repetition, and repetition, forming a self-similar structure nested in a certain level. The main meaning of "hetero" refers to diversity, fragmentation, and chaos, forming an irregular, disorderly structure. “Complex but not complicated†or “heterogeneous†is not true or complete complexity [13]. The complex form of the fractal pattern is generated by a simple mathematical formula, which not only greatly enriches the content of the picture, but also profoundly reveals the relationship between the simple and complex contradiction and mutual transformation in the dialectic. The complexity is simple. Simple, revealing complexity. The fractal pattern contains a fine layered nesting system. When viewed from different scales and distances, or even at different times, the changes in the structural unit can be found, and new feelings can be obtained. This is not available in traditional textile prints.
4 The irreplaceability of traditional textile printing patterns 4.1 The irreplaceability of printing technology At present, the traditional printing method is still the mainstream of industrial textile printing. Digital inkjet printing is used for proofing and small batches of personalized textiles because of its short development time. printing. Fractal patterns usually require digital inkjet printing to express their fine structure and rich colors. If the traditional printing method is used to simplify the processing by color separation and other graphics, the fractal pattern will be lost, which will not reflect its beautiful appearance. Personalized style.
4.2 Irreplaceability of creative methods Traditional textile prints are generally designed and designed by art designers with aesthetics and drawn by hand-drawn graphic design software. The production of fractal patterns is fundamentally different from general digital graphics. Although some software (such as UltraFractal, FerryMan Fractal, etc.) can create fractal patterns through interactive interfaces, it is not simple to design fractal patterns suitable for textile printing. Feel free to create menu commands. These efforts have increased the difficulty of creating designers who have not been involved in the field of mathematical knowledge, thus limiting its promotion and application. At the same time, the graph generated by the mathematical formula presents a regular and mechanical aspect within a certain range.
4.3 The irreplaceability of cultural connotation The fractal pattern generated by the digital law is not restricted by ethnic groups, regions and individuals. It has universal applicability in the world and has certain advantages in the design of modern textiles that pursue internationalization and rapid response. But at the same time, the products of this technology lack the feelings of national traditional culture, and there will be certain cultural connotations in the classic artistic expression. Therefore, the nationalization and personalization of such digital graphics requires the continuous efforts of scientists and artists, and its perfection will go through a long period of time.
5. Conclusion The creation of fractal patterns has changed the design concept of traditional textile printing patterns, and the patterns exhibited have strong visual impact and attractiveness, which can be realized by the technical means of digital inkjet printing. Its infinitely fine hierarchical structure and partial and global self-similar features have made a new interpretation of visual graphic aesthetics, and also provide an unusual creative approach to the design of textile print designs in the "formal beauty" rule. By comparing the fractal aesthetics between the fractal pattern and the traditional textile print pattern, the fractal pattern no longer appears in a mysterious mathematical concept and form, but can be well understood by the designer, in the textile The intersection of the pattern design is extended. As an innovative design element of textile printing patterns, fractal patterns have broad application prospects in addition to their artistic value, realizing the digital design of textile printing patterns, in line with modern personalized and diversified consumer demand.
While the fractal pattern presents a good development trend, there are still many problems to be solved. By analyzing the limitations of the fractal pattern, it is conducive to deep research and explore its aesthetic value from the perspective of artistic aesthetics.
References: slightly
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