We've been playing around a lot with fractals this week, partly because so many of them happen to look Christmasy, and partly because they make for a good break from our usual math lessons while still keeping us on our toes.
One of the things I really like about fractals, apart from the mind blowing detail of their representing infinity in a finite space, is the simplicity of their design. Take the Koch snowflake for instance, iteration after iteration the pattern appears more and more complicated, ultimately creating a ridiculously intricate design. But, on closer inspection, the entire figure is made up of one simple pattern, repeated over and over again.
Repeat the pattern three times...
...and you can put it together to form a star (the 2nd iteration of the Koch snowflake).
Repeat it 48 times, and you can puzzle out the 4th iteration snowflake (assuming of course you have a fair amount of free floorspace and plenty of popsicle sticks).
We have a good deal of floor space in our basement family room (just terrible lighting for picture taking), and I had a couple of teens to keep busy, while I crafted with their younger siblings, so puzzling out a snowflake seemed like a perfect project for them.
Puzzling is the right word too, because even though the snowflake looks like a six sided shape, it's really just a triangle. Keeping that fact (and the sides) straight is quite a brain teaser. The girls used a protractor to check their angles (all the points form the 60° angles of an equilateral triangle)...
...and double checked their completed project (a solid hour of worth of work for my 15 year old - while her 13 year old sister wandered away to craft with the younger sibs), by measuring across from point to point. The final snowflake was a little squished, but it was difficult to see where...
...until we (being a puzzle fanatic, I couldn't help jumping in when A abandoned ship) used loose craft sticks to outline the triangles from the first...
...second...
...and third iterations (or phases) of the snowflakes. Suddenly, we could see the shape in a whole new way...
...and were able to straighten it right out, and piece together smaller versions of the second iteration star, and third iteration snowflake in the center with no trouble at all. Which brings me to my favorite feature of fractals...
...they're just so pretty!
7 comments:
I think my kids would really enjoy this!
I like the popsicle stick version even more.
They are indeed very beautiful and your daughters should get a medal for staying on task for such a long time!
Yes, they are so pretty! We are studying Islamic art this week and these snowflakes remind me of the shapes in Islamic art! It is interesting how our studies often relate!
Angelic Scalliwags - It's amazing how quickly an hour can slip away when your working a puzzle. But, it was definitely too long a project for my middle schooler.
We have to try this popsickle version, the result is very beautiful!
No way we would have space for this, but the end result looks amazing!
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