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GEOSTATS: Question on Fractal

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  • Mohammad J Abedini
    Greeting all, I have a question on the sufficiency and necessarily condition for a process to be fractal. Let me first raise the question and then provide some
    Message 1 of 1 , Nov 14, 1997
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      Greeting all,

      I have a question on the sufficiency and necessarily condition for a
      process to be fractal. Let me first raise the question and then provide
      some background.

      Geometric object: Island
      Variable 1: Area of Island
      Variable 2: Perimeter of Island

      Is that ok to say that Island is a fractal object if the relationship
      between variable 1 and 2 in log-log space is linear?

      It seems to me that delineation of fractal object have gone through two
      totally different routes with similar end results.

      Route 1: Measuring the length or area and/or volume of an object with
      different spatial unit (i.e., length=ruler, area=pixel, and volume=voxel)
      and then finding a power law relationship between say perimeter of
      coastline and different length of ruler.

      Route 2: Measuring the area and corresponding perimeter of say a few
      Islands and then observing a power law relationship between these two
      variables. In this approach, if I am right, we are not concerning about
      different spatial unit such as different grid spacing or ....

      Is this a correct understnading of fractal geometry?

      Your comments is greatly appreciated.

      Best of luck
      Abedini




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