A Pop-Up Sierpinski Valentine Card

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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.

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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.

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

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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.

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

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Repeat, making four new rounded cuts.

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And then tucking in the folds.

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

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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:

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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.

    http://extremecards.blogspot.com/2009/02/fractal-pop-up-valentine.html

  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

    http://tweetphoto.com/6011983

  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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