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.
- 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.