Archive for February 12th, 2009

A Pop-Up Sierpinski Valentine Card

February 12, 2009

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.