Geo @ ObjectGraph

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In this semester, my professor handed out an interesting homework about finding fractal patterns in nature shapes. Fractal is mathematical patterns which seems to be appearing at random but it starts revealing repeatitive features as you zoom in / out. For example, you can find fractals in galaxy, brain’s neuron, and shorelines. They all look same if you zoom in one part. Once you zoom again, they show similar shapes. If you zoom in a edge in a coastilne, you will see similar patterns of zig-zag shapes again. If you zoom out, you will see similar shape in the big picture.

Fractal and Zooming - Image Source: Wikipedia

Benoît Mandelbrot

Oddly, when we started this homework, Benoît B. Mandelbrot just past away in the same week. He is a famous mathematician from Poland and he did great research about mathmatical aspects of fractal. Since my graduate course is about GIS topics, we are excersizing on computer but this homework assignment does not require any digitized media. If you are curious about this problem, please try this at your home.

Coastlines are fractal or not?

Things to prepare

  1. Printer and Papers
  2. Compass - If you do not have it, use a paper clip or a string. Bend the paper clip in V shape.
  3. Download two PDFs
    1. Long Island, North Shore
    2. Graph Paper

Compass - Source: Wikipedia

... or bend a paper clip!


  1. Print out two worksheets (PDFs).
  2. Take 2km distance from the scale
  3. From the left end of shoreline, take one step and set your compass where the compass intersect with the shoreline. This is your first interval.
  4. Take another interval with the equal distance as previous step. You had 2 intervals now.
  5. Repeat the previous step and count the intervals until you reach the right edge of the shoreline.
  6. Record the number of steps in the first row of the table.
  7. Go to step 2 and take the next longer distance, 4km. Follow the same steps. You will have smaller number of steps.
  8. Go to step 2 and take the next longer distance, 8km. Follow the same steps. You will have smaller number of steps.
  9. Go to step 2 and take the next longer distance, 16km. Follow the same steps. You will have smaller number of steps.
  10. Plot the number in the log scale graph.

How to take steps


If the shoreline is nature / fractal pattern, you might see a straight line in the graph.

Extra Credits

Can you find any fractal nature objects around you?
If you want, try to print out shorelines around your country. Check if they will show fractal feature in the shapes.


This exercise demonstrated a method to reveal fractal patterns in nature and the procedure is very simple which you might apply on other objects around you. To pursue my computer science background, I would like to write a little Python program in the next posting.

Long Island North Shore

Reference and Data Source

About Assignment: This assignment is from ERS 501 course which taught by Dr. Kennelly in Long Island University and I would like to thank him for introducing this problem. I would like to note that this blog entry is my personal article and the contents were recreated based on my perspective. This is nothing to do with LIU’s official website or it does not represent course materials or its quality.

About Graph Paper: The graph paper was printed from .

About Coastline: Long Island’s Shapefile is from NOAA: National Oceanic and Atmospheric Administration (NOAA), National Ocean Service (NOS), Office of Coast Survey, and the Strategic Environmental Assessments (SEA) Division of the Office of Ocean Resources Conservation and Assessment (ORCA)
Publication_Date: 1994

Publication_Time: Unknown
Title: NOS80K: Medium Resolution Digital Vector U.S. Shoreline shapefile for the Gulf of Maine GIS project

Other Links: Fractal (

Thanks: Soe San invented the paper clip solution for me.


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