分形信息论及其应用

本文简述分形信息理论及其应用，解决了在分形几何学中悬而未解的问题，即什么是分形，什么是分形维数。本文所引进的分形示性数，分形维数与分形维谱统一与概囊了人们熟知的相信维数，容量维数、盒计数维数、信息维数与Ｒｅｎｙｉ维数。最后通过倍周期分支通向混沌之示例说明分形信息度量之应用，揭示分形信息论与分形几何学之间本质差别。分形信息论为复杂模式与图象之研究提供了新方法。

Fractal Information Theory and Application

Through fractal information theory, this paper addresser an important unsolved problem in fractal geometry, i.e., what is the exact definition of fractal and its mea.sures. It will be solved by thd introduction of a series of new concepts and formulas of fractal information measures such as fractal entropy, fractal index, fractal dimension and fractal spectrum which include and unify similar dimension, capacity dimension, box-count dimension, information dimension and Renyi dimension. Fractal information theory is applied to chaos research to illustrate the essential difference between fractal geometry and fractal information theory. The results suggest that this new theory can open up a new prospect in the analysis of complex objects and digital images.