Koch Snowflake cards

Like most self respecting nerds, I love fractals. So what better way to celebrate winter than creating a fun card based on the famous Koch Snowflake (also know as the Koch star and island)!

A fractal is a geometric figure that has some pretty awesome special features. They have "self symmetry," creating detailed repeating patterns that are often described as "the same from near as from far." They're found all over the place in nature and are used in math and science in a variety of applications. 

One of the easiest to create by hand, and also one of the easiest to understand, is the Koch Snowflake. First described by Helge von Koch in 1904, this fractal is based on an equilateral triangle. To build it one, you create an equilateral triangle, then remove 1/3 of one side of the triangle and replace it with an new, smaller equilateral triangle. You repeat this process on each side, then repeat it on each side of each new triangle, and so on. The result is a shape that can literally have infinite perimeter, but finite area. Cool right?

So, for an extra nerdy card, I used the Koch Snowflake shape and created a fun, glittery pop up.

The process is simply to make a Koch snowflake template, trace that into a card and cut around the shape with a craft knife, leaving the shape attached to the base at a few points. Then fold the pop up in the opposite direction of the card, creasing the contact points carefully. Finish by backing with contrasting cardstock to create the front of your 4.24" x 5.5" card.

To make it more festive, I created snowflake "covers" that were just the Koch snowflake. These I embossed and glittered to make them stand out beautifully. I also used the inside of the double snowflake to create a custom stamp, simply tracing it onto craft foam and cutting it out, then adhering it to an acrylic block with some double-stick tape. I used it as I would any other stamp. This card reads "Baby, it's cold outside."

Now, I'll have really detailed instructions up on CRAFT soon, I hope, but in the mean time, why not just grab my templates and make a card the easy way?

Print the PDFs below onto cardstock and cut until your heart's content!

• Single Koch snowflake pop up card
• Single snowflake cover
• Double Koch snowflake pop up card
• Double snowflake cover

If you have a digital cutter, like I do, this all becomes very easy, indeed! I have an old first generation Silhouette from Quickutz. You can pick them up for about $100 on eBay, and they are amazingly useful. I use the free software Inkscape to design my digital cutting files and then the free software for the Silhouette to manipulate and cut the shapes. It's totally awesome!

Anyway, if you have such a machine, all you need to do is download the appropriate DXF or SVG file and let your computer do the work for you! You may opt to throw in a perforation or scoring line down the center when you cut to make folding easier, but I just used my Scoring Board. Now you can make cards for all your nerdy friends!! Huzzah!

• Single Koch snowflake pop up card (dxf)
• Single snowflake cover (dxf)
• Double Koch snowflake pop up card (dxf)
• Double snowflake cover (dxf)
• Single Koch snowflake pop up card (svg)
• Single snowflake cover (svg)
• Double Koch snowflake pop up card (svg)
• Double snowflake cover (svg)

Anyway, I hope you have fun. Be sure to share pictures of your cards!

MORE fractal cards!

After I made the last fractal Christmas card, my daughter pointed out that it also looked a lot of like a pile of present. (Kids!) So I decided to play with that idea a bit.

I selected a set of coordinating scrapbook papers, and cut the inside of the card just as I did last time. For a quick review...

For this version, it's important to measure and cut accurately, so that the pieces we cut for "presents" fit well. That said, go ahead and cut a second insert from a piece of plain or scrap cardstock. We'll use this for templates. Just cut along the folds.

Then it's time to trace and cut. We'll need one large piece as the central present. Then cut three of the mid-sized present, one from each of three types of paper. Lastly, cut nine small pieces -- two each from the three different papers and three from the last.

Now, we get to play paper tetris. Ink the edges of all the the present pieces, so that they have some depth when attached. Use a bit of glue stick to attach the paper pieces onto the base. Then attached the base to the outside of the card. Ink the edges and you're nearly done.

I added some strips of paper for "ribbons" and attached the inside to the outside. Then I gave the front a bit of decoration.

Add the sentiment and I'm good to go! This got me thinking, what other fractal-based patterns can I cut and make into cards. As it turns out, I am not the only one who is obsessed with this technique. Yale offers a fun free pattern using blocks. They actually have a whole lab activity using Cantor sets to make fractal folds. There is also a book called "Fractal Cuts" by Diego Uribe, that you can buy new or used on Amazon. (Yea, I totally ordered it.) So I played with another boxy design.

Then using the same template method as above, I made another "present" card.

Fractal Christmas Card

We've been studying fractals with the Kaleidoscope Cooperative for Science and Math. As part of that study, we explored Sierpinski's Triangle, a fractal in which equilateral triangle shapes are removed according to a specific set of rules, forming a repeating pattern.

I wanted to extend the 2D version we made in class to a 3D project. Luckily, I found the Fractal Foundation and their instructions to create a triangle fractal cutout. By making repeated cuts in folded paper you can create a shape similar to a Sierpinski's triangle. And when you're done, it looks like a Christmas tree. Which makes it a most excellent holiday card!

The kids had a great time making these, but I wanted a little more refined version for my nerdier friends and family members. So I pulled out my craft supplies. For this project you need: colored cardstock, a ruler, a pencil, scissors, a glue stick, a star punch, an embossing folder and embosser, and assorted inks.

I started by cutting a piece of green cardstock to 8.5 x 5.5 inches. I folded this in half to create a 4.25 x 5.5 inch card. Using my ruler I marked the middle of the card and drew a line from the folded side to midway across.

Then I cut along the line, folded one section away from the folded edge and creased well. Then I unfolded the flap and inverted the tab, pushing the fold inwards.

Refolding the paper, and tucking the tab inside, I once again used my ruler to measure the halfway point on each of the side "steps." I drew a line halfway across the step. Then it was cut, fold, invert.

 I repeated the cycle once more. After this point the paper was too thick to fold and cut neatly. I you used copy or origami paper you might be able to get more detail.

Once all the tabs were done, I used the edge of my ruler to crease them really well. Then I un-inverted the folds to flatten the paper and ran the card through an embosser. I also trimmed the paper by 1/4" all around and inked the edges. When that was done, I carefully refolded the tabs to create the pattern and sprayed the front with gold ink.

I cut a piece of red cardstock to 8.5 x 5.5 inches, folded it into a 4.5 x 5.5 inch card and embossed that as well, inking the edges when it was done.

I applied glue to the back of the triangle tree and carefully attached it to the inside of the red card, pressing down well and being sure to center the green card. I punched a little star from yellow cardstock, folded it in half and used the glue to attach it to the top of the tree. I then decorated the front of the card with some scrap green cardstock and another yellow star.

All I need to do is add a cheery sentiment and this card is ready to add a bit of geek chic to someone's Christmas.

Super Simple Sailboat

Our most recent Science and Swim at Belvidere Pool was the most well attended yet! Perhaps the article in the Warren Reporter helped. This week we made sailboats with easy-to-find materials and lots of awesome duct tape then set them afloat in the pool. I swear the toddler pool looked like it had spawned an armada!

To set the mood, let's start with your morning earworm: "Come Sail Away" by Styx.

Now that we're all humming along together, we can get building! First you need to assemble materials: A tray to act as the hull (we used small cardboard ones donated by Nature's Harvest), a bamboo skewer to act as the mast (a small dowel or pencil will also work), lots of colorful duct tape, a small amount of modeling clay, scissors, wax paper for the sail and an old foam egg carton for the rudder.

You start by covering your hull with duct tap, top, bottom and sides. If you want, you can also build up the sides a bit with tape, to prevent water from coming onboard.

Now you need to attach the mast. Make a small ball with the clay and place to towards the bow of the boat. Then stick the skewer into the clay. Mold the clay around the skewer to hold it in place. Cover this well with duct tape. If you have the time and ability, punching a hole in the hull and pushing the mast through a bit, then adding a bit of glue and covering with duct tape will add more stability to your design.

Next we need to attach the sail. I chose wax paper because it's relatively waterproof and inexpensive. That means you can try lots of different sail shapes, if you like. You don't have to stick with the standard rectangle. Try a circle or triangle or a octagon, if you like! Attaching the sail is very simple: just cut two slits in the paper with scissors and slide it onto the mast. If you plan to change shapes often, using a bit of tape to build up spots on the mast to hold the sail in place will suffice. For more longevity, use a bit of scotch tape to hold your sail onto the mast. In either case, be sure to create a "cup" in the sail to catch the wind.

Over the course of our build at Science and Swim, we experimented with lots of ways to make our sails sturdier, as it was pretty windy. One mom had a great idea: putting a strip of duct tape on the top and bottom of the wax paper to add stability. We also experimented with creating tie lines with tape and using materials like old plastic bags and ziplocks for sails. You can even build a sail out completely of duct tape. This is where prototyping is important! Keep modifying that design until you get it to do what you want!

It's also fun to add a rudder, so that you can steer your boat. (This also illustrates an important idea about fluid mechanics, by the way.) To make the rudder, just cut a piece of foam from your egg carton, cover it with duct tape and cut out a small wedge. Then make a slit in the back of your boat and fix the rudder in place. By changing the angle of the rudder, you can change the direction of the boat. It's a lot of fun to experiment with different rudder shapes too!

Then it's time to take the boat to the water and give it some wind! If you have rough waters, you will need to replace your sails, as the wax paper will eventually break down and start to fall apart.

One creative young man, used leftover egg carton pieces to make fun characters for his boat. You can too!

Have fun and enjoy sailing the high seas... or your backyard pool!