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 finished collecting the data for the Richardson Plot for finding the dimension of Great Britain, finding it to be approximately 1.23 (compared to the 1.25 that Mandelbrot reported in his essay How Long is the Coast of Britain?.
From there, we considered the border between Spain and Portugal and looked at three maps at different levels of detail. We used measurements taken from those maps to find the dimension of that border, and then considered a question of history. Richardson wrote that one country has historically given the length of the border as 987 km, while the other has given a length of 1214 km. Your assignment is to decide which country is which, and why might this difference have a logical basis simply on how the countries measured the border, and could have nothing to do at all with politics.
The next reading assignment from Fractals: The Patterns of Chaos is from pages 83-92: “Fractal Math Imitations, Both Fanciful and Real.” Please have that section read by tomorrow.
We continued yesterday’s applications of the Richardson Plot to the Koch Curve and finally to the coastline of Great Britain. The results of these can be found here.
For Friday, please read the section in Fractals: The Patterns of Chaos from pages 83-92 (Fractal Math Imitations)
We finished calculating dimension of various fractals, and observed that our Generalized Hausdorff Dimension formula still falls short when a fractal is not perfectly self-symmetric. There’s still work to be done.
We also got a textbook of sorts, the book Fractals: The Patterns of Chaos. We will occasionally have reading assignments out of this book, the first of which is pages 61-73, the section on fractal dimension. Please read this section by Monday.
Tomorrow, we will have our Fractal Art Show Gala Opening! Remember to bring your snacks!