一类推广的平面Koch曲线的解析表达式

Analytic Expressions of Flat Koch Curves Promoted by A Class

实际问题研究中一些自然现象需要用各种分形曲线来进行模拟,为了清晰了解分形曲线,就需要寻找其分形曲线的解析表达式.黄雪梅运用迭代函数系IFS来构造分形的方法研究了von Koch曲线.本文将经典Koch曲线迭代系统中的等边三角形推广到任意夹角的等腰三角形,并利用相似压缩变换,即通过不间断地将区间[0,1]进行等分迭代的方法,得到了该推广形式的Koch曲线的解析表达式,并验证了经典Koch曲线的解析表达式是本文结果的特例.

To Study some natural phenomena,it requires that use fractal curves to simulate. For better understanding fractal curves,it needs to obtain the analytical expression of fractal curves. By means of iterated function systems( IFS),Huang Xuemei research on the von Kochcurve. This paper extend equilateral triangles to isosceles triangles which have free angles between the bottom and the waist in iterated systems of the classical Koch curves,and by virtue of similar compression transformation,that is,uninterrupted uniform iteration for the interval,we get the analytical expression of generalizations of classical Koch curves and verify that analytical expression of classical Koch curves is a special case of the above result.