Meeting 4. Fractals

For this week, we'll be playing with code that riffs on the classic Sierpinski fractal and exposes intriguing and surprising connections from fractals to other parts of mathematics, including chaos and dynamic systems, iterated function systems, cellular automata, number theory, binary/ternary number representation, space-filling curves, and more. It is all quite magical!

To complete before meeting

• ✅ Download starter project for your assigned group, review README.txt
• ✅ Add code to get basic version working

See Ed post for more detail on above tasks.

Further resources and fun

If you have finished the code and have some extra time and further curiosity…

• Why Sierpinski is the fractal of Halloween
  • https://blogs.scientificamerican.com/roots-of-unity/a-few-of-my-favorite-spaces-the-sierpinski-triangle/
• Grant Sanderson of 3Blue1Brown produced two delightful videos that tease out the connections between Sierpinski, counting in binary/ternary, and the Towers of Hanoi. The fabulous Keith Schwarz makes a guest appearance, too.
  • Part one: https://www.youtube.com/watch?v=2SUvWfNJSsM
  • Part two: https://www.youtube.com/watch?v=bdMfjfT0lKk
• Just for fun, a fractal poem
  • http://larryriddle.agnesscott.org/ifs/poem.htm
• These two resources were a great source of inspiration for this meeting:
  • Ian Stewart, Four Encounters With Sierpinski's Gasket
  • The mother of all Sierpinski resources: 270 pages of non-stop action that explores every nook and cranny relating to Sierpinski https://www.oftenpaper.net/sierpinski.htm
    • archived version: https://web.archive.org/web/20230524212903/http://www.oftenpaper.net/sierpinski.htm