摘要： 介绍了分数维图形的理论基础及其显示算法,并应用到自然树木的三维显示中。指出了迭代函数系统不仅是复数域的一种非线性变换,而且可以是计算机语言所描述的一个过程,甚至可以是一个抽象的过程,只要对它的运动、变化规律作出合理的图形学解释,就可以显示其分数维几何形态。同时,复域的迭代函数系统可以显示出千变万化的色彩与图形,研究其内在规律性,并生成所希望的数学艺术图形具有一定的应用和理论意义。

关键词: 分数维图形, 非线性映射, 吸引子, 混饨, 真实感三维图形显示

Abstract: This paper introduces the theory foundation and the display algorithm of the fractal graphics, which has been applied into the three dimensional display of the natural tree. It demonstrates that the iteration function system not only is the nonlinear transformation in the complex domain, but also may be a procedure which is described by the computer language or even more an abstrct procedure.If only do we make the reasonable graphics interpretation for its moving, changing rule, the fractal geometry graphics could be displayed. At the same time, the varible color and graphics could be viewed through the iteration function system in the complex domain, and it has the practical theory and application value in the aspect of studing the inner rules as well as generating the hopeful mathematical arts graphics.

中图分类号: 

• TP391.4