方型Koch曲线的定义、分维及性质

The Definitions, Fractional Dimensions and Properties of the Square Koch Curves

文中定义了基本方型Koch曲线和方型Koch曲线,计算了它们的分维(相似性维数),证明了方型Koch曲线的分维集在区间〔1,2〕中稠密。这样就可用方型Koch曲线来研究和描述任意分形曲线的某些性质(如曲线的复杂程度)。

The paper definited the fundamental square Koch curves and the square Koch curves, and calculated their fractional dimension (similar dimensions) and proved that the square Koch curves are dense everywhere in the interval [1,2]. So we can use the square Koch curves to consider and describe some properties of any fractional curve (for exemple, the complexity of curves).