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Author Topic: Fractal Dimension Index  (Read 8043 times)
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muis
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« on: October 26, 2006, 11:11:34 AM »

Can anyone please give me a basic clear cut outline on how to go about calculating the fractal dimension.
Thanks. smiley
« Last Edit: October 12, 2013, 04:00:22 PM by Nahee_Enterprises » Logged
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« Reply #1 on: October 27, 2006, 07:34:31 AM »

The term "fractal dimension" is sometimes used to refer to what is more commonly called the capacity dimension (which is, roughly speaking, the exponent D in the expression n(epsilon)==epsilon^(-D), where n(epsilon) is the minimum number of open sets of diameter epsilon needed to cover the set).  However, it can more generally refer to any of the dimensions commonly used to characterize fractals.

   http://math.bu.edu/DYSYS/chaos-game/node6.html

Fractal Dimension (D) quantifies the scaling relation among patterns observed at different magnifications.
  • For Euclidean shapes for a line (D = 1)) and encapsulated filed area such as a square (D = 2).
  • For Fractal patterns, D lies between 1 and 2D = 2 for the Mandelbrot set.
  • As the complexity or irregularity of the repeating Fractal structure increases; D approaches 2.
  • D is related to how fast the estimated measurement of the object increases as the measurement device becomes smaller.
Excel Spreadsheets:
  http://www.wseas.org/2002.xls
  http://www.wseas.org/2003.xls

REFERENCES:
Rasband, S. N. "Fractal Dimension." Ch. 4 in Chaotic Dynamics of Nonlinear Systems.  New York: Wiley, pp. 71-83, 1990.
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Jules Ruis
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« Reply #2 on: October 27, 2006, 03:59:53 PM »

For more information about the Fractal Dimension see also:

http://www.vanderbilt.edu/AnS/psychology/cogsci/chaos/workshop/Fractals.html

Jules.
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Jules J.C.M. Ruis
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