Week 7: Mandelbrot Set and Complex Numbers

Partial view of the Mandelbrot set.
Partial view of the Mandelbrot set. (Photo credit: Wikipedia)

This week we are going to learn about one of the most famous fractals, the Mandelbrot set

  • In class, we watched more of the NOVA special on fractals: http://youtu.be/LemPnZn54Kw?t=20m12s (from the start to about minute 24)
  • We then talked about iteration, and found that to make good pictures, we need complex numbers.
  • As an introduction to complex numbers, from minute 3 to minute 9: http://www.isallaboutmath.com/complexnumbers.aspx — sorry that I couldn’t edit out all of the places where he says it’s “easy”
  • Finally, we got to multiplying complex numbers (which we usually have google or wolfram alpha do for us), and that will get us what we need for the mandelbrot set!
  • You also might like this video, which makes me think I’d be a better teacher if I knew more about video production: http://www.youtube.com/watch?v=aP4fWMLofvo

Also, I’m looking for some help

  • I need about 60,000 business cards, which means I am seeking misprints, cards from businesses that have changed addresses, etc. If you have any ideas for sources, can you ask them? Or connect me to them? This is for a geometric sculpture project, which we will make a start on later this semester.
  • I am looking for someone who is interested in working on a fairly simple visualization of a googol and a googolplex (very large numbers!). If anyone is interested, we could find a way to make this count as a project.
  • I am also looking for someone who knows a little something about video production for a project I am thinking about doing on asking questions in mathematics. It’s an ill-formed project at this point, so I’m looking for someone who might be willing to bounce ideas around with me. If you are a someone like this, or you know someone, let me know!

And

  • You should be working on a project of some sort! The assignments are under “projects” on the top banner of this page.
  • Let me know if you need any feedback on anything!
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