GEOSTATS: Question on Fractal
- 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
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
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