Introduction: Clay Koch Snowflake

About: Mostly a programmer and random computer guy, but like to mess with hardware and other real life objects sometimes.

Evil Mad Scientist Laboratories wrote a thing on how to make a Sierpinski triangle out of fimo (or other) clay. I liked it a lot and made a few, which turned out so-so. They also asked what other fractals could be made this way. I experimented a bit and think I've found a reasonable way to make a Koch Snowflake.

This run didn't turn out terribly well. I was using Sculpey clay that's been laying in my drawer for several years colored with food coloring. The food coloring didn't take too well, nor show up in pictures well. The clay itself gets very non-pliable and prone to cracking if left alone for a while after working it into decent shape. It's not a good material for the job, but very cheap (and in my case on hand already). I also have very modest skills in handling any kind of clay. Still, I'm writing it up because I feel the theory is sound and I know myself well enough to know that I won't be getting around to getting better materials or more time. I do so hoping perhaps someone else with more materials, time, patience and skill would care to elaborate/rewrite/expand on this.

Update: Evil Mad Scientist has an alternative write up now with more pro-looking pictures and illustrations using food items, if contemplating making this checking it out would be a good idea.

Step 1: Theory

After some sketching, I realized that several equilateral triangles could be assembled into a shape similar to itself in such a manner that if it was done again, it would converge on one side of a Koch Snowflake. The image speaks for itself kind of (excuse the not-so-3117 photoshop skills) - a dark colored triangle is placed in the center and four more (combined into opposite facing parallelograms) are stacked on the outside. A twice as wide triangle is then stacked on top, making the whole thing into a triangle that can be reduced and reused in the same manner again.

Step 2: Start

Make a dark equilateral triangle of a size you can later reproduce. I here went with 1/4 inch due to working on 1/4 inch graph paper, but any size will do. Then make enough light similar size stock to cut/make into four pieces of similar length. Don't be to greedy on size, because a lot of clay will keep being added. Even small starting pieces will grow exponentially (with a pretty good size exponent, only a little shy of quadratic) so start fairly short.

Step 3: Stack

Stack these as in the original sketch into a two parallelograms surrounding a different colored triangle. Then make a twice as wide (still equilateral) triangle and stack it on top, making a 3x base width triangle. If you made the smaller triangles from a predefined source (those playdough squeezers, for instance) you could also make five of the original size and make the big one that way.

Step 4: Extend

Carefully extend this triangle until it is the same shape as the original triangles were. You will most likely need to cut off some of the ends if they deform, which is fine - this thing will grow quickly over the iterations anyway.

Step 5: Chop

Cut the extended piece you have just made into four pieces (again, don't be shy about trimming off bad parts). Make a piece of dark to match them - same as the first one you made.

Step 6: Reassemble

Assemble these pieces as per step 3 and make another twice wide top piece. Note that direction matters now - the dark part of the triangles need to go down or toward the dark center. Proceed to repeat the steps until you are here again. You might want to chop off some length (possibly to save and see past iterations) because it will grow in length fast as mentioned before and I doubt you will need all the stock from further iterations.

Step 7: Done, Kinda

The pictures here and in the intro are third iteration. I was already losing shape and getting blurry, but no doubt in part due to poor materials and a lot of start-stop losing the fluidity of the clay with no way to regain it (can't exactly work it into a smooth state again). To make a complete snowflake, attach three slices (the last iteration can be left without the top triangle as below if you'd like, or put it in a triangle instead of a hexagon but it won't extend beyond it) to a triangle of dark three base widths wide, i.e. the same size as each iterations assembled state prior to extending.

Bake as described on package (I didn't bother this batch since I wasn't happy enough with the result) and use for whatever (Evil Mad Scientist again goes into more detail in their article).

As you can see, mine turned out less then optimal but I see no particular reason this shouldn't work. If you're the more artsy type, perhaps you can demonstrate it better. If you're the math type, perhaps you can demonstrate why I'm wrong/right about it.

Happy claying.

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