分形理论应用研究若干问题及现状与前景分析

Some questions in the applications research of fractaland analyse of its present situation and foreground

讨论了分形理论中几个主要的理论分支即分形维数计算、分形插值、分数布朗运动、分形测度、幂指数分布、自相似性与标度不变性在各种实际研究领域中的应用,描述了这几个理论分支的数学模型,及在关联学科中的应用。指出了分形理论应用研究目前主要还是以上述几个理论分支为基础,应用于计算机图形学、数据处理、物理学、化学、生物学、地质统计和矿产预测等领域,提出未来分形应用的发展前景将以多重分形、分形动力学、统计分形和随机分形等为主要理论基础的观点。

Discuss the applications of some main embranchments of fractal theory: calculation of fractal dimension, fractal interpolation, fractal brownian motion, fractal measure, power exponent distribution, self-similarity and scaling invariance in the kinds of areas of practics, the mathematical models of these embranchments are discribed, some applications in some subjects related with it are introduced.The application research of fractal theory presently are based on the embranchments above,can be applied in computer graphics, data processing, physics, chemistry, biology, geological statistics, mineral prognostication.The foreground of fractal application future would be chiefly based on multifractal, fractal dynamics, statistical fractal and random fractal.