Fractals & Chaos Recap for 10/22

We continued yesterday’s applications of the Richardson Plot to the Koch Curve and finally to the coastline of Great Britain, largely confirming Richardson’s findings as included in Mandelbrot’s article. The results of these can be found here.

Also, at the end of class today, we discussed the border between Spain and Portugal and looked at three maps.  Take the data below and answer the following questions:

  1. What is the dimension of the border between the two countries?
  2. One country has historically given the length of the border as 987 km, while the other has given a length of 1214 km.  Which country is which, and why might this difference have a logical basis (in other words, why might the countries have truly measured the borders in this way? The answer isn’t political!)
Step Size S C Distance measured
100 km 1 7.3 730 km
50 km 2 16.2 810 km
25 km 4 35.4 885 km
10 km 10 93.2 932 km
5 km 20 200.6 1003 km

Remember: for Friday please read pages 61-73 of your new book Fractals: The Patterns of Chaos

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