A Pop-Up Sierpinski Valentine Card


sier-12Last 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.

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13 Responses to “A Pop-Up Sierpinski Valentine Card”

  1. jd2718 Says:

    xkcd’s version does not seem to have been actually cut out, just a diagram. Plus, no godzilla.

    This is still the best sierpinski valentine card on the net.

  2. Ξ Says:

    Hey, it’s a trend!

  3. Carol Says:

    Way cool. Mine has the hearts set at an angle so you can’t do this so-much-easier folding method.


  4. Ξ Says:

    Carol, I really like your version! Thanks for sharing it!

  5. Math Teachers at Play #1 « Let’s Play Math! Says:

    […] activities — do yours? Xi at 360 blog offers step-by-step instructions for constructing A Pop-Up Sierpinski Valentine Card. I’ll have to bookmark that for next […]

  6. Andrés Says:

    I did the straight one, but I folded it the other way around


  7. Carol Says:

    Oh….Wow, I REALLY like the Christmas tree with the folds going to the back. Nice one Andres!

  8. FERNANDO Says:

    ASWESOME info, can’t wait till Valentines!

  9. Patricia Says:

    My math teacher’s a huge xkcd fan (as am I), and he had us make these in class for extra credit. (I failed the last unit test so I suppose I am making Sierpinski valentines today!)

  10. Valentine’s Day, send Mobius Hearts our Way! « Number Loving Says:

    […] good look round 360′s blog and don’t miss the pop-up Sierpinksi Valentine’s cards here, all about […]

  11. The Sierpinski Valentine, Cardioids, and Möbius Hearts « Math Munch Says:

    […] Really though, nothing says “I Love you” like a Möbius strip. Am I right? Here’s a quick little project you can do to make a pair of linked Möbius hearts. You can find directions here on a blog called 360, or you can watch the video below. Oh, and as if that wasn’t enough great stuff, here’s one more project from the 360 blog, a pop-up version of the Sierpinski Heart! […]

  12. What Do Valentines and Math Look like/Sound Like? | Cold Spring Harbor Educational Foundation Educational Resources, cshedfoundation.org Says:

    […] Make a pop-up Valentine Fractile! […]

  13. Mr G's Idle Musings » Blog Archive » My Diigo 02/14/2013 Says:

    […] A Pop-Up Sierpinski Valentine Card « 360 […]

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