摘要
本文研究平面上有面积的曲线的分形性质及其在ｄ维欧氏空间Ｅ￣ｄ中的推广．对瘦分形曲线，分维Ｄ＿ｆ＝ｌｎ２￣ｄ／ｌｎ（２／ｋ￣（ｌ／ｄ）），而对于胖分形曲线，分形指教β＝－ｌｎｋ／ｌｎ２．α＝ｄ．ｄ＝２时的胖分形曲线包括经典的Ｐｃａｎｏ曲线为其特例。
This paper studied the fractal properties of the curve having area on the plane and itsgeneralization in the d-dimensional Euclid space E￣d.For thin fractal curves, the fractaldimension D_f = log2￣d/log(2/k￣(1/d)),for fat fractal curves,the fractal exponents β=-logk/log2,α=d. When d=2, the fat fractal curves include classical Peano’s curvedrawn by D.Hilbert.
基金
国家科委重点科研项目和四川青年科技基金
