What is a fractal? I won't try to answer that, except for one observation: the defining characteristic of a fractal is self-symmetry. Should you wish a more complete answer, you'll find an interesting and complex journey ahead of you, filled with some truly stunning pictures.

Self-symmetry means that, as you zoom in or out on the fractal, you find shapes that are similar to the fractal when viewed at other scales. Most mathematical objects become flat and boring as you zoom in on them indefinitely; not fractals.

This presents an obvious construction technique for a manual fractal, when taken in reverse. Form a pattern, shrink the pattern, copy it a few times to form a new pattern, then shrink the result, and repeat. Without further ado, I give you the Sierpiński triangle, rendered in edible form:



Setting out to craft this most tasty fractal, I knew I needed a proper medium to work in. I used the rolled butter cookie recipe from The Best Recipe:
2 sticks butter
1c superfine sugar
1/2 tsp salt
1 lg egg + 1 yolk
2 tsp vanilla
2 1/2 c flour

For the superfine sugar I used confectioner's sugar: not a substitution I would normally make, but I was more concerned about texture than anything else. The last thing I wanted was sugar crystals mushing up the boundaries of my fractal. I made the dough with only 2c flour, then split it into two batches. For the light half, I then added the remaining 1/4c flour. For the dark half, I instead added 1/4c cocoa powder. For the same reason as I used confectioners sugar, I also sifted both the flour and the cocoa powder.



Having made the dough, I began construction. First, I formed the basic set of triangles:



And then stacked them to form the first iteration:



The next step is where it gets tricky, and I'm afraid I didn't have a companion to take pictures. Essentially, the dough is then stretched, making it longer and thinner while preserving the form -- thus scaling down iteration 1. The tricky part is that if the dough is too warm, it just turns to mush; too cold, and it tears. The ideal temperature, of course, lies between refrigerator temperature and room temperature, and can be maintained quite easily for periods well in excess of 76 milliseconds. The key appears to be to only stretch the dough a little bit at a time; the mere act of picking it up and setting it back down is almost sufficient, with a little bit of working it by hand to maintain an even cross-section. As it gets longer, I cut it in half, then in half again, finally resulting in four sections of dimension similar to my starting triangles. One of these is discarded, and a new triangle of dark dough is added. These are stacked, forming iteration 2:



For the sake of completeness, I should point out that the ends will get all mushed up; they need to be trimmed up to look nice. Here's iteration 3, immediately after stacking:



But, a little bit of trimming, and it looks much nicer:



Iteration 4 is much the same process; details are now getting relatively fine:



Alas, either through poor technique or fundamental limits of the medium, iteration 5 is rather mushy and poorly defined. It's also starting to have rather more dark dough and less light dough, predictably.



The detail in iteration 5 is actually most easily seen post-cooking. It's a little blurred, but all 5 steps are visible if you look closely:



One of my favorite things about this technique is that I'm actually implementing the generation algorithm in cookie dough, rather than simply drawing in great detail. The complexity of the fractal is thus an inherent result of the process, rather than of the precision with which the artist (or computer program) draws it. As a corollary, the amount of work I do is proportional to the number of iterations, rather than the resultant complexity. Something about this seems to me to be the way fractals Ought To Be Generated. And the computer scientist in me is tickled to see exponential complexity resulting from a linear number of operations.

If I were trying this again, I'd put some effort into finding a tastier dough (which I blame nearly entirely on my modifications; I'm sure the original butter cookie recipe was better). It's not bad, but it's somewhat bland and boring; it's also not sweet enough for my taste.

The inspiration for this praxis comes from the Evil Mad Scientist Laboratories. They also did a version of the Sierpinski carpet in cookie dough, though they wimped out and only did 3 iterations.