Research And Application Of Fractal Geometry In Clothing Pattern Design

Clothing pattern design has the close relationship with clothing, it can play a role ofdecoration and beautification for apparel. With the development of social economy,people’s concept and attitudes of consumption and aesthetic for clothing are changing.Clothing are not only required because of keeping warm and covering nude, but also hashigher requirements in the aesthetic. Fond of novelty, human beings are constantly pursuitof beauty and focus on the aesthetic, which provides a broad development prospects forclothing pattern design. Fractal is mainly used to study the complex patterns of naturalthings，it is a new branch of mathematical geometry. According to the fractal mathematicalalgorithms, it can produce infinite fractal graphics which have great visual impact, andtheir artistic charms are self-evident. Therefore, the application of an attractive graphicalfractal pattern design to fashion has become a focus of concern. However, the patterns offractal are rich and diverse, so they aren’t easy to be controlled, which brings a lot ofdifficulties to people in the application.Based on the study of fractal theory, this article researched systematically generationmethod of fractal images, and focused on structural characteristics of several categories oftypical fractal images. Analyzing the mathematical principles, it summed up structuralvariation law of some basic graph, this paper paid an emphasis on analyzing therelationship between Julia fractal images and various parameters based on GLCM. Thespecific conclusions obtained are as follows:1．Julia fractal images are the petal-like, we can infer preliminary that the number ofpetals showed by high-level Julia fractal images depends on times of Iterated function,which means a graph generated by n order iterated function shows n petals. Julia fractalimages is sensitive to initial values c, every different values c will form completelydifferent fractal graphics. Petals are symmetrical, and to some extent each petal is almostexactly the same. 2．The number of petals of Mandlebrot fractal graphics depends on the power ofiterative function, which means a graph generated by n order iterated function shows n-1petals. The greater the n is, the greater tendency to round graphics have, when n is infinity,the graph is a circle.When n is even, the graphs are symmetrical about x axis. When n isodd, graphics are symmetrical about the origin. On the whole petals are evenly distributed.3．The number of petals of Newton fractal graphics also depends on times ofIterated function, which means a graph generated by n order iterated function shows npetals. The flower shape are basically symmetrical,and to some extent each petal is almostexactly the same. With the number of iterations increasing, the center red zone is graduallyincreasing.When the number of iterated function is in the range of3to10, the number ofpetal is different, but the graphic shape and color are basically the same.4．The article focused on analysis of the relationship between Julia fractal images andvarious parameters based on GLCM. For the escape time limit k, the graphical energyvalues reduce as k decreasing, entropy values increase with the increasing of k, eventuallyleveling off. For the escape radius limit m, the energy values of the graph reduce with theincrease of k, eventually leveling off. The higher times of Julia are, the smaller the entropyis. The entropy value changes more gently.For fractal images generated by the IFS methodor based on L system, and some types of fractal graphics, designers can modify a fewparameters to generate entirely different fractal images, and complete the storage of pictureand other related functions. Combining the law given, designers can draw ideal fractalgraphics by fractal software more quickly and easily. To further study the influence ofvarious parameters on graphical grain structure and fineness.In addition, this article designed a generation system of fractal graphics, established asimple and easy-operation communication interface on VB6.0. With this system, we canget various types of fractal images, including some fractal graphics based on recursivealgorithm, the Mandelbrot fractal graphics, Julia fractal graphics and Newton fractalimages on the escape time algorithm, and what based on iterated function systems.Finally, the article made a second design for fractal graphics combining fashiondesign software and image processing software, then fractal graphics are applied toclothing pattern design, and gives the specific effect chart.