Kaleidoscope Learning: fractal

Tuesday, December 31, 2013

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!

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!

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

Monday, December 30, 2013

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.