A Pop-Up Sierpinski Valentine Card

Last year we made interlocking Möbius Valentines.  This year we’re going staying three-dimensional, and making a pop-up card that forms a Valentine Fractal!

Start by taking a sheet of paper and folding it in half.

Next, you want to make a cut along the fold.  Measure halfway along the fold, and then make a cut of half the width.  Since you’re going to want to form a heart, make  it a bit rounded like the top of the heart, and then fold it over to make a crease.

Once you’ve creased it, refold that bottom part so that it sticks into the middle of the card, like this:

Now iterate!  Along the original fold, measure halfway down each part and cut ¼ of the width (instead of ½), still forming the top of a heart.  As before, fold those pieces down to create creases.

And then refold along those creases to tuck the folds inside:

Repeat, making four new rounded cuts.

And then tucking in the folds.

And again!  Cut, fold over, and tuck in.  And here’s the result!

Happy Valentine’s Day Everyone!

You can also make a plain old traditional Sierpinski Triangle with this method.  Just make straight cuts instead of rounded ones, and it ends up looking something like this:

I first saw this design in the book Fractal Cuts by Diego Uribe, published in 1994, although according to this article from Mathematics Teacher (which includes a template) it might be older than that.   In those instructions you do all the cutting and folding first (without tucking the pieces into the center) and then push out the pop-up part all at once at the end, but I found that to be really frustrating; tucking in as you go along is a lot easier.  As far as I know the Valentine variation is my own doing, but it’s certainly possible that someone else has done it before.

Tags: Sierpinski heart, valentine's day math