Tag Archives: vihart

Koch Snowflakes

Came across Sal‘s discussion of the Koch Snowflake (on wikipedia) yesterday.

Got a little obsessed and wanted to draw it programmatic like I did 20+ years ago when I first saw the Sierpinski Gasket on a NOVA tv show (which I re-did using Khan’s software a few months ago).  After a few failed attempts (and a failing to recognizing my usage of sine and cosine), today I went and looked for someone else’s code just to get me through it (oh the aging brain!) and found N-Wing’s code over at everything2.

Here it is: Koch Snowflake Fractal (Doh, WordPress isn’t allowing me to embed the program right here in the blog).

Vi Hart shows them in her Triangle Party Doodling too if you like her style (who doesn’t?).

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Howto Try Trihexaflexagon

We finally managed to get a hexaflexagon working!  Check out the video of my son demonstrating.

If you’re having trouble getting started too, here’s a recap of our journey.

We were introduced to them a few weeks ago thanks to vihart‘s great video (via my friend Kate), but stumbled around at first trying to figure them out.   We watched Danny Halvern’s Hexahexaflexagon movie and had some success putting them together with a compass and ruler but it was very time-consuming and we didn’t get many iterations before giving up.  We read over the hexaflexagon construction instructions but were still overwhelmed.  We found a page that talked about the different ways to flex it, but it was still too much to get us off the ground.  I went back to basics and read Martin Gardner‘s original Scientific American Book of Puzzles and Games which probably would have worked if I had taken the time doing it myself, but couldn’t work trying to get the kids to do them as well.  I found a template (and was confused by the having both sides on one side) but, didn’t have a colour printer available so was stumped again.  How were we ever going to get folding?!

And along came the Celebration of Mind Gathering for Gardner.  Their party organizer’s kit finally collected together a simple set of Trihexaflexagon templates in the same spot that we could work with.  We printed out numerous of their blank templates (note to self: modify this to include the numbers for the absolute newbs) and after a few attempts at numbering and colouring it for the kids we got one put together.  Woot!  My son has already modify it to include putting the pattern in the middle and watching it go to the outside and he wanted to do two more before bed, but there is plenty of time for it now.  Are hexahexaflexagon’s next?

Update: Day Two.  We’ve made a few more videos as we worked through our folds and more.  First up is me walking you through the tri and the hexa hexaflexagons.