Fractals & Chaos Recap for 10/23

After discussing the reading from the text and the answer to yesterday’s question of the border between Spain and Portugal, we moved on to the last method of finding dimension, the Box Count method.

This method of finding dimension produces the same table of values and log-log plot that we made with the Richardson plot, but the values of S and C are found using a different method. Imagine overlaying a grid on top of a fractal image. We then count (C) the number of boxes of that grid that contain some portion of the fractal. We then repeat this process using a grid with smaller boxes, the sizes of which relative to the original give us S.

The YouTube channel 3Blue1Brown has a great video summarizing all of this.

After enough counts are collected at different scales of boxes, we can create a log(c) vs log(s) plot and find the dimension using the slope as we did before. Your homework is to make the necessary counts with the coastline of Great Britain.

Also homework: For Monday, read pages 83-92 in Fractals: The Patterns of Chaos (about fractal math limitations)

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