بعد كسيري
11.5 x 200 = 2300 km
28 x 100 = 2800 km
70 x 50 = 3500 km
Figure 1. As the length of the measuring stick is scaled smaller and smaller, the total length of the coastline measured increases.
البعد الكسيري هي نسبة تعطي إشارة إحصائية حول التعقد. قد يحدث البعد الكسيري عدداً غير سليم.
مقدمة
Figure 2. A 32-segment quadric fractal scaled and viewed through boxes of different sizes. The pattern illustrates self similarity. The theoretical fractal dimension for this fractal is log32/log8 = 1.67; its empirical fractal dimension from box counting analysis is ±1% using fractal analysis software.
دور المقياس
Figure 4. Traditional notions of geometry for defining scaling and dimension.
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(1)
Figure 5. The first four iterations of the Koch snowflake, which has an approximate Hausdorff dimension of 1.2619.
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(2)
D هي ليست واصف منفرد
Figure 6. Two L-systems branching fractals that are made by producing أربعة new parts for every 1/3 scaling so have the same theoretical
أمثلة
التقدير من بيانات العالم الواقعي
انظر أيضاً
- List of fractals by Hausdorff dimension
- Lacunarity
- Multifractal analysis
- Fractal derivative
ملاحظات
الهامش
- ^ Balay-Karperien, Audrey (2004). . Charles Sturt University. p. 86. Retrieved 9 July 2013.
للاستزادة
- Mandelbrot, Benoit B., The (Mis)Behavior of Markets, A Fractal View of Risk, Ruin and Reward (Basic Books, 2004)
وصلات خارجية
- TruSoft's Benoit, fractal analysis software product calculates fractal dimensions and hurst exponents.
- A Java Applet to Compute Fractal Dimensions
- Introduction to Fractal Analysis
- Bowley, Roger (2009). "Fractal Dimension". Sixty Symbols. Brady Haran for the University of Nottingham.
