【作者】 袁杰；

【导师】 刘大昕；

【作者基本信息】 哈尔滨工程大学 ， 计算机软件与理论， 2002， 硕士

【摘要】 分形是描述自然界和非线性系统中不光滑和不规则几何形体的有力工具。大量事实表明，分形广泛存在于自然界，分形涉及的领域已遍及数学、物理、化学、材料科学、生物与医学、地质和地理学、地震和天文学以及计算机科学等。分形的研究既有重要的理论意义，又有广泛的应用价值。 本文在对生成分形图形的逃逸时间算法进行分析和研究的基础上，重新定义了逃逸时间函数，提出了加速逃逸时间算法。经过大量数据验证，此算法在保持原精度不变的情况下，使算法效率得到明显提高。用新算法绘制的分形图形精彩动人，令人赏心悦目。作者又在本文中提出了两个关于广义Mandelbrot集和Julia集的猜想，并通过绘制大量广义M-集和J-集图形得到验证，作者还对广义M-集的一些性质进行了证明。 此外作者在分形理论的应用方面进行了研究，根据L系统的原理使用VB语言编制了L系统演示程序，并用此演示系统实现了对自然界中植物树木的模拟。另外作者按照迭代函数系统(IFS)的思想，采用迭代算法，仅用少量的数据就生成了象山貌这样复杂的自然景物。这些工作成果在军事指挥、动画制作、自然景物模拟、建筑配景、虚拟现实等方面都有重要应用价值，而如果采用传统的绘图方法需要大量的数据，浪费空间和时间。更多还原

【Abstract】 Fractal is a powerful tool that can describe roughness and irregular geometric shapes in the nature or in the non-linear system. Many facts show that fractal widely exists in the nature, and spreads all over fields such as mathematics, physics, chemistry, material science, biology and medicine, geography, earthquake and astronomy, computer science and so on. The research on fractal has both important theoretical significance and extensive applied value.Based on the analyses and study of the constructing fractal image’s escape time algorithm, this article redefined the escape time function and provides the accelerated escape time algorithm. Through a great lot data validation, keeping the aboriginal-precision, this algorithm makes the efficiency increase prominently. The graphs drawn by the new algorithm, make you feel well. The author brings forward two supposes about general M-set and J-set that are proved by constructing lots of general M-set and J-set . The author also testified some characters of general M-set.Moreover, the author researches on the application of fractal theory and codes the L-system demonstrating program, according to the theory of L-system, by using VB program language, which simulates the plant image in the nature well. Furthermore, according to the Iterated Function System(IFS), the author, using iterated algorithm, only uses few data to make up complex natural sceneries like mountain appearance, and it can be greatly used in command of military affairs, making cartoon, decorating architecture, virtual reality, and so on. While if using the traditional graphing method, it needs lots of data, moreover, wastes store and time.更多还原