Theme for the Day: Fractals

Remember my earlier post on fractals?   Well, I'm truly hopeless at this point, so I need to share my obsession.

So what are fractals anyway?

Wiki says:  a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole, a property called self-similarity.

Well (for the non math people like me) that basically that means layers of repeated shapes that can be calculated by a formula.  But you don't need a formula to enjoy them.  Check these out:

• Fractals in nature and even in the garden 
• Fractal art gallery on Cool Math
• Also check out the wiki link for some lovely examples

Ready to make your own?  Try these cool (free!) online generators:

• "Snowflake" style - design your fractal with five straight lines
• Cool Math has five
• Easy Fractal Generator lets you draw a Julia or Mandelbrot set (or a custom one if you are mathematically inclined) and lets you export your finished work to a file for printing.  Nice.
• This generator is similar to the snowflake one above but lets you overlap fractals and export the finished work
• Sierpinski Triangle

Hands on and fun links for the younger kids:

• this pbskids.org    project 
• The fractal foundation project
• Sierpinski Triangle color page
• Sierpinski carpet (cubes) color page
• Sierpinski gear (circles) color page
• A youtube.com search for "fractals" will give hundreds of results
• Fractal your dinner with the unusual  Romanesco cauliflower (see the details here - scroll down)
• Fractal cookies!  (Okay - a brave parent will have to help with this)
• Fractals in clay  (again better to stick with fewer iterations- repeats- with the little ones)

For the older kids and the lesson planners:

• pbs.org has a wonderful fractal lesson from Nova episodes including:
• A generator
• An article on Benoit Mandlebrot
• A fractal lesson that includes an interactive and a   discussion of fractals 
• A working video link to an interesting story about fractal analysis of tapestries
• You might notice the link to the Nova episode Hunting the Hidden Dimensions which is no longer available on PBS.org.  It is available for free on Hulu however. 

• Hoagies has some recc'd some interesting sites also.

Downloads

• A caltech worksheet for the Sierpenski Triangle. Notice! This is a word doc that will want to immediately download.
• A PDF worksheet on fractal math from fractalmath.com, advanced HighSchool+
• A PDF worksheet from Randoff College for grades 5-8
• Open Source software to download. Note: I have not trialed, so use at your own risk.
• A trial copy of (not-free) fractal software. Note:  I have not trialed, so use at your own risk.