Research On Two-dimensional Fractal Graph Generation Algorithm

With the fractal technology booming development, graceful and colorful 2D fractal figure is gradually applied in advertising design, virtual game, textile industry, landscape planning and many other fields, enjoying wide and bright prospect.This paper firstly introduced the emergence and development of fractal theory, its geometrical characteristics, its relation with computer, and its application in real terms. To be continued, several common algorithms to generate 2D fractal graph have been comprehensively summarized, with sufficient reviews and detailed verification of their feasibility. At last, the OpenGL(open graphical library) has been adopted in VS2010 to implement the popular L system algorithm, by which the common 2D fractal graph was accurately simulated. In terms of L system algorithm, the basic principle, classification, algorithm design and implementation were introduced. As to the classification of L system algorithm, improvements were made on the L system algorithm for certainty of simulation of 2D fractal graph. It mainly aimed at generating the graph plotting within regular parameters in L system. Some mathematical curves(such as sine wave and cosine wave, tangent wave, circular, etc.) or other graphs were used to replace the straight line between two points, making these 2D fractal graphs able to play the role in different fields and scenarios and by different ways of improvement. In the aspect of generation of 2D fractal graph in random L system algorithm, the paper introduced various parameters of the control system L algorithms, by randomness of which the randomly generated 2D fractal graph in L system becomes applicable in much wider range.The research and study of 2D fractal algorithm mainly aimed at making improvement on generation of 2D fractal graphics in L system algorithm in terms of the features of simulation of real objects. By means of experiments, the improved L system algorithm in the paper was testified to be effective for simulating 2D fractal figure, and such types of figures could be applied in wider fields.Not only can it more accurately describe the natural characteristics of algae, but also simulate the fractal patterns used in textile industry or advertising design.