How To: Make Sierpinski Carpet Cookies

Make Sierpinski Carpet Cookies

How to Make Sierpinski Carpet Cookies

Since it is now the holiday season, I thought we could spend this weekend making some baked goods that have mathematical patterns on them. In this post, we'll look at making cookies that have a fractal pattern based off of a modification of the pixel cookie technique.

The people at Evil Mad Scientist Laboratories wrote a blog entry a couple of years ago on making fractal cookies based off of the Sierpinski Carpet. They used chocolate dough to make the "holes" in the design.  

How to Make Sierpinski Carpet Cookies

They've also posted an entry on how to make fractals using clay with the same technique. Here the results are much more precise.

How to Make Sierpinski Carpet Cookies

On Sunday, I decided to follow their recipe for making fractal cookies, but I used red paste food coloring to color the dough for the holes.

How to Make Sierpinski Carpet Cookies

Materials and Tools

  • Cookie dough (I followed a recipe similar to the one used by the Evil Mad Scientists)
  • Food coloring (The Evil Mad Scientists used chocolate)
  • Baking sheet
  • Parchment paper
  • Sharp knife
  • Oven

Making the Fractal Cookies

Roll out eight logs and use your hands and a working surface to form them into square prisms. Use a sharp knife to trim the edges. The ones I formed were about 3 inches long.  

How to Make Sierpinski Carpet Cookies

Form a few logs of your alternate color. You will need as many of these as you are making iterations.

How to Make Sierpinski Carpet Cookies

Surround the alternate colored log and squeeze the pieces together. A tiny bit of water could help here, but be careful not to add too much.

How to Make Sierpinski Carpet Cookies

Stretch keeping a square cross section. You will have to press and roll hundreds of times. Here I stretched out to 4 times the length. I'd really only recommend twice the length. Trim off the edges using a sharp knife.

How to Make Sierpinski Carpet Cookies

Cut evenly into pieces.

How to Make Sierpinski Carpet Cookies

Now stretch each of these and form into the next iteration. You'll have to use the eight pieces to surround another full sized alternate color piece.

How to Make Sierpinski Carpet Cookies

Stretch and cut.

How to Make Sierpinski Carpet Cookies

Stretch and cut again and again, until you have 8 evenly sized pieces.

How to Make Sierpinski Carpet Cookies

Use these to surround another full sized alternately colored piece.

How to Make Sierpinski Carpet Cookies

Press and stretch a little bit until you have a nicely formed fractal. Use a sharp knife to cut out the cookies.

How to Make Sierpinski Carpet Cookies

Bake and serve.

How to Make Sierpinski Carpet Cookies

Show Off Your Work

If you make these cookies or any of the other previous Math Craft projects, please share with us by posting to the corkboard. Maybe you just have something cool that you made or saw on the web—you can share that, too!

If you like these types of projects, let me know in the comments. If you have any other ideas you would like to pursue, let me know in the forum.

Next post, we're going to make some fractal cupcakes.

2 Comments

Epic!

And tasty! It's also pretty cool because this is the way a lot of mathematicians (and especially physicists) think about the fractals that form in the phase space diagrams of chaotic nonlinear dynamical systems. They talk about the stretching and folding of phase space. This is exactly what you are doing when you form these cookies. You are stretching the dough and then folding it back into itself by cutting and reforming it.

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