# Mandelbrot Redux: Day 1

Ok, sorry, that last post was mean-spirited. I assure you that I’m 100% unicorns and rainbows now; it’s just, the end of the year, you know? My seniors have graduated, and I now have one (1) student in calculus for the next week. What are we going to do? He chose to go on into some more Calc II material, because he plans to take a few classes at UIowa next year.

So, here we are at the end of May lunging head long into infinite series. What does this cherub see on the super cool intro page to the chapter (you know, the only full color page that shows an apple dropping and fighter jet being totally awesome)? A freaking fractal.

He says, “let’s make those.”

I say, “Son, get the computers.”

Over the next week I will be providing you all a play-by-play of how this student and I build the Mandelbrot set from scratch. I promise that you’ll get the source code and that it will be usable by you and your students. I’m geeking out pretty hard right now.

Riled Up: Here’s the Steaming Pile of “Nitty-Gritty” You Ordered Episode V: Striking Back With Students In Mind

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6 thoughts on “Mandelbrot Redux: Day 1”
@Mike: Thanks! Unfortunately, post-AP is the only time I have to integrate the arts. There is actually a whole college course about the physics in Tom Stoppard’s plays: http://physics.weber.edu/carroll/honors/

Blog? No, not yet. Maybe. Funny, I’ve been thinking about it over this past week, now that school is winding down and I want to keep track of ideas for next year, and to reflect upon the year starting in September. And then Kate Nowak and Sam Shah both posted about starting blogs. They just might provide enough inspiration to get me started.

@Shawn: We don’t have the resources for a Mathematica license either. In a perfect world, we all would be using industry-standard software with our students.

@Frank: Great information. Lots to look at for next year. Very interested in your use of the arts for your AP classes. Do you have a blog?

And be sure to check out:

http://opinionator.blogs.nytimes.com/2010/03/07/finding-your-roots/

and:

http://vimeo.com/660866

We use VPython in my AP Physics C class all year. Kids write their own simulations. After the AP exam, we discuss fractals, chaos, determinism, and entropy. We watch “Run Lola Run,” read Tom Stoppard’s play “Arcadia,” and write some VPython programs about chaos in populations (Val’s grouse from “Arcadia”) and also programs to create the Mandelbrot and Julia Sets (There is a Coverly Set in “Arcadia.) Here are two handouts:

Chaos in Populations:

http://docs.google.com/Doc?docid=0AYh2KfPMJ6ONZG5nZHY4bl80NzZkdmtxeHBjZw&hl=en

Fractals in Arcadia:

http://docs.google.com/Doc?docid=0AYh2KfPMJ6ONZG5nZHY4bl80NzdmbTczOXpjOA&hl=en

VPython has be great for the kids to use: real simple, dynamic typing. The iteration used to animate motions and interactions really helps them when they get to integrals in calculus. Here’s a simple example of a bouncing ball:

http://vpython.org/contents/bounce_example.html

BTW, there is program called Sage which seeks to be a viable free open source alternative to Magma, Maple, Mathematica and Matlab.

http://www.sagemath.org/

Been discussing sequences in my senior applied mathematics course and skimmed the surface of basic fractals. Unfortunately the looming standards mathematics exam has cut out any extra computer lab time to discover these things of beauty in a hands-on way.

I’m interested to see how this turns out and how much elbow-grease is required to develop the Mandelbrot.

Are you using Mathematica?

@Mike: We’re actually using PHP. The student is also currently in my programming course as well, and that’s the language he knows best. I’m toying with teaching him a more computationally friendly language like C++. Our school won’t buy me a Mathematica license… :( Do you guys have it at your school? If so, how did you wrangle that?

=shawn