We discussed the reading from Fractals: The Patterns of Chaos and looked at some references to the “Butterfly Effect” in popular culture. We spent most of the rest of the period playing with the Solar System simulator online.
For Monday, please read pages 49-54 from your book, the section on “The Fractals and Chaos of Outer Space.”
We started watching a Nova documentary on The Strange New Science of Chaos. It’s from 1989, but it has held up well and serves as an excellent introduction to this strange new world of constrained randomness and sensitivity to initial conditions.
For Friday, there are three sections from Fractals: The Patterns of Chaos that I would like you to read:
- Pages 55-60 – Our Weather Today is Chaos
- Pages 93-97 – Chaos and Symmetry Hybrids
- Pages 99-106 – Chaos Sculpts Fractal Landscapes
Today, used the Box Count method to find again the dimension of Great Britain (report your findings here) then completed one last project to find calculate the dimension of one of the spiral fractal seen on the last dimension calculation sheet (this took most of the remainder of the period).
For Monday, read pages 83-92 in Fractals: The Patterns of Chaos (about fractal math limitations)
If you’d like to rewatch Adam Neely’s Coltrane Fractal video we saw in class (or check out some of his related videos), click the link.
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)