بعد كسيري

(تم التحويل من Fractal dimension)

Coastline of Britain measured using a 200 km scale
11.5 x 200 = 2300 km
Coastline of Britain measured using a 100 km scale
28 x 100 = 2800 km
Coastline of Britain measured using a 50 km scale
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 يكون البعد الكسيري عدداً غير صحيح.

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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%[1] using fractal analysis software.



دور المقياس

Lines, squares, and cubes.
Figure 4. Traditional notions of geometry for defining scaling and dimension.

 

 

 

 

(1)

A fractal contour of a koch snowflake
Figure 5. The first four iterations of the Koch snowflake, which has an approximate Hausdorff dimension of 1.2619.

 

 

 

 

(2)


D هي ليست واصف منفرد

Figure 6. Two L-systems branching fractals that are made by producing 4 new parts for every 1/3 scaling so have the same theoretical as the Koch curve and for which the empirical box counting has been demonstrated with 2% accuracy.[1]


أمثلة

التقدير من بيانات العالم الواقعي

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ملاحظات

الهامش

  1. ^ أ ب Balay-Karperien, Audrey (2004). Defining Microglial Morphology: Form, Function, and Fractal Dimension. 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