Starting a HS Fractals class that will use Mathematica

[PhillyWilliams]

I'm new to the forum (this is my first post), so if this isn't a new question, my bad!

Next year, I will be teaching a trimester length class to high school seniors that will be an introduction to fractals.  The plan right now is to have them use NCTM's (old) book Fractals for the Classroom by Peitgen, et al, as it's a great over-arching introduction that's very readable (you can find it here: http://amzn.to/kZiCjB ).  The end project is to get the kids using mathematica (I have some code for them to use, thanks to Getz's Graphics with Mathematica, so it's not like they'll have to create it on their own) to generate some images.  

To be brief: Has anyone done anything like this before?  Does anyone use Mathematica to work with fractals and produce images?

I'm still working on the syllabus, but I want to make sure we get to talk about Infinity, Iterated Function Systems, Dimension, and the major mathematical questions that surround fractals in addition to using computers and computer programs to construct fractals.  My personal strengths are in the theoretical mathematics, as I'm not the best programmer and definitely couldn't teach any programming languages, so I'm not looking to try and bring in any Java or the like to this course.  

So, I'm just interested in if anyone else has tried something like this and, if so, with what success.  I'd also love to hear other ideas on what a good introduction to fractals should include, or other ways to make this the best possible course.

Thanks all!

[DarkBeam]

http://bugman123.com/Hypercomplex/index.html

Here you find sample Mathematica 3D fractals

[Fractal Ken]

http://classes.yale.edu/Fractals/ is a good resource.

[David Makin]

I'd love to be able to work on fractals in Mathematica - I just can't afford it !
(I couldn't even afford it at student rate)

AFAIK the best academic source on the web is the link Ken gave you, plus maybe start here for L-systems:

http://algorithmicbotany.org/papers/#abop

[Babilon]

To be brief: Has anyone done anything like this before?  Does anyone use Mathematica to work with fractals and produce images?

Hello, I programed some time ago a package to make fractal images with Mathematica.
You can find that in "The Wolfram Library Archive" in the MATHSOURCE section.

The direct link to the package is

http://library.wolfram.com/infocenter/MathSource/6733/

The package makes image and contours representations of The Julia set, The Mandelbrot set and The Newton Set all of them with arbitrary order.
It is possible to use the colouring patterns used in mathematica in funttions like DensityPlot etc.

There are two versions of the package, one for Mathematica 5.2 and the other for Mathematica 6, 7 and 8.
In the .zip archive are the package file, a .txt file with simply intalation instructions and a Mathematica notebook file with some examples to test de posibilities of the package and to see the easy of use.

The code in the package may be helpfull for you to program other fractals and other things related to fractals.


I hope that this will can help you. 

I'd love to be able to work on fractals in Mathematica - I just can't afford it !
(I couldn't even afford it at student rate)

It may be helpful for you too.



PD. When I have some time may be I will improve the package to take advantage of the multiprocessing capabilities of the last versions of mathematica to improve the speed.

[PhillyWilliams]

Many thanks, all, for the help!

I've been using and enjoying the Yale site for a while (didn't Mandlebrot make that site while he was there?), but I'm glad it got in this thread.

Babilon -- thanks for the notebook!  It really will help a lot -- I've been trying to come up with distinctly mathematical ways of showing the kids those sets through mathematica, but I still want the ability for them to fluidly create/interact with images, and I think that notebook hits those points, which is awesome.

On another note, turns out each student in the class will get an iPad for the term (I'll be teaching this class in the spring), so I'm super excited about how I'll be able to approach iteration and the infinitely scalable with some of the pretty darn intuitive apps that are out there.  My hope from there is that once we get an almost mechanical feel for some of the structures and processes, that will help the students understand the pure math that's behind them.