Friday, January 14, 2011

Fun With Fractal Geometry

Sierpinski's triangle, an equilateral triangle, filled with smaller, and smaller, equilateral triangles, is an intriguing contradiction of infinity bound by a finite shape.

It's also a fractal. And, fractals are fun. They enable computer aided designers to create stunning lava flows (like in Star Wars III), or believable looking icebergs, and flying penguins. They hold the promise of opening doors for weather forecasters, geographers measuring coastlines, cancer researchers, and even environmental scientists.

And, they're really pretty - perfect for rainy day, boredom buster, doodling, and coloring.

Of course, all that measuring of equilateral triangles, is bound to make a person hungry. It's always good to have a snack on hand (even if it's not quite mathematically correct).

I won't give a step-by-step for the cookies. They've been done before, and they're pretty self explanatory. We used rolled out dough, cut into 1/2 inch triangles, and then pieced together, to make the pattern. Until we got tired of working with the tiny triangles, and started making them bigger, which ruined our end result some, but didn't hurt the taste.

Next time I think we'll try The Fresh Loaf's Mad Scientist inspired, rolled refrigerator dough method. (See, I'm not the only one, who likes to turn everything under the sun into a cookie!)

Want to know more about fractals? I suggest checking out Nova's Hunting the Hidden Dimension, or Arthur Clarke's Fractals, The Colors of Infinity. They both offer a nice taste of what fractals are, and why they matter, in a way even younger children can appreciate, and enjoy.

It's great to be a homeschooler.


Christy said...

I love that you turn everything into a cookie. I would have LOVED math if it involved cookies. I seem to have blocked out any memory of fractal geometry. Very interesting.

Phyllis said...

You knew that I would love this post that combines math and treats!
Did you see Mathwire's post today on Pascal's Penguins? I so thought of you when I saw it!

Raising a Happy Child said...

Seriously you should write a book about "Bakeschooling". Fractals are truly fascinating, and I like the art created with triangles.

An Almost Unschooling Mom said...

Raising a Happy Child - If I wrote a book, I wouldn't have all this time to bake :)

Phyllis - Thanks for the heads up - I'm clicking over to check it out!

Jessica said...

Have you seen this girls website and her doodling videos? It's awesome.

Check out the infinity elephants one for fractals. She's on youtube, also.

Joyful Learner said...

Is there such a thing as fractal time? If so, then you can do all the baking and write a book! :)

I think I might have been absent when they taught fractal geometry because it doesn't ring a bell. But I do remember watching a commercial on TV where it showed another TV inside which showed another TV inside it which was my first ah-ha! moment with infinity. Once again, infinity in a finite box.

Sparklee said...

Great projects! I'm on a mission to convince my son that math isn't boring, and your blog is a great inspiration!

Ticia said...

As long as you don't get into proofs I like geometry and that is the best kind

Debbie said...

I love Natalie's and Christy's comments. Seriously you should write a book on Bakeschooling! Maybe it is something to think about when you don't have the children to homeschool!

MariaD said...

I featured your photo in this “Inspired by calculus: Dimensions of holiday craft” collection at

Thank you!