Fractal cookies, from Evil Mad Scientist Laboratories
Take nine "square cylinders" (i. e. rectangular solids which are much longer in one direction than the other two) of dough, one of which has chocolate in it.
Arrange the nine sticks in a three-by-three grid with the chocolate one in the center; squish them together so that they are one big piece of dough.
Stretch the whole thing to eight times its current length; cut into eight pieces of equal length (the length of the original piece), each of which will have a chocolate center. (This can be done by stretching to twice the length, cutting in half, and repeating twice more.)
Add a piece of chocolate dough of the same size; again arrange in a three-by-three grid with the chocolate one in the center, stretch, and cut. Then do it again. Then cut the whole thing into slices and cook.
Of course, you get the Sierpinski carpet in cookie form.
However, at the level of iteration given here, (8/9)3, or about seventy percent, of the cookie will consist of non-chocolate dough! This is sad. I recommend interchanging the chocolate and non-chocolate doughs.
See also the Sierpinski gaskets made from polymer clay, which are made by a similar process. These are inferior, because they cannot be eaten.
10 April 2008
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Optimal strategy is to break the initial cookie dough into two blocks: one light, one dark. Then, as you progress, you use up each in the same proportions, ending up with mostly light and mostly dark cookies, both. And you use up all your cookie dough.
This is going to be highly entertaining, but I think that the ones done in bakeable clay are going to be more interesting.
A cooler item would be to implement a transform that is more complicated, say to get a fractal leaf.
Not to name-drop like JVP here, but the moment I saw that recipe I was brought back to the chaotic dynamics class I took ## years ago with Jim Yorke. Always with the emphasis that sensitive dependence (and thus chaos) hinged on "stretching and folding".
Brilliant! I can't believe I haven't thought of this before--I think I know what I'm bringing to the math department picnic this year.
I disagree that using more chocolate would necessarily be better, though--the white dough has cream cheese in it.
Ooh, another option (which might require some dexterity, but I think it could be done) is to only use two copies of the previous iteration, one on either side of the new chocolate piece, to get a nice representation of the Cantor set. With some care, I think it would be possible to roll out each iteration without flattening it too much, and then you'd have a greater proportion of chocolate to non-chocolate.
I read this recipe was taken from a 700 year old recipe written by an Orthodox Greek monk on the island of Cyprus, who discovered fractals while planting carrots and lettuce in patterns.
This is disputed by the island's Turkish population who believe you can find the recipe in the Koran or at least in Arabian Nights.
I thought fractal cookies would be almond bread (or mandelbrot) in the shape of the Mandelbrot set.
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