Receta Chocolate Chip Mandelbrot for an Exercise in Mandelbrot Fractal Generation
The problem with loving baking is that if you have a sweet tooth, well, it is hard not to partake of your own hard work. It is a hobby with consequences. As a result I am always looking for reasons to bake for other people.
So when my husband got all excited at discovering a fractal (remember he is a math/computer science guy) with the name Mandelbrot, and asked me to bake mandelbrots for his class in conjunction with an assignment he gave them, I jumped at it. One of his co-workers observed that it was a lot of my time/effort for a relatively small joke (which made me laugh), but John knows I am always happy to have a reason to bake. And these cookies are not difficult.
If you are curious, this is what a Mandelbrot fractal looks like. This particular image was generated by John and used with his permission. When I asked him what I could say to explain what a Mandelbrot fractal is, this is what he told me: The Mandelbrot fractal, named after the mathematician Benoît Mandelbrot, is based on “imaginary numbers” (remember the square root of -1?). Each point (pixel) of the picture represents a particular imaginary number, and is colored based on whether that number passes certain mathematical tests. Because of this, drawing it is entirely an exercise in (fairly simple) calculations — it doesn’t require any artistic ability what-so-ever. My students were told how to make the shape, and were then able to experiment with different formulas (using cosines and such) to change around the color scheme.
You understand perfectly now, right? Especially where he says it is an exercise in fairly simple calculations? Ha!
So about the actual cookies. As many of you probably know, the mandelbrot cookie is an Ashkenazi Jewish cookie, very similar to the Italian biscotti, although in some traditions the bread is not sliced and baked a second time (I have only encountered this twice, but ironically this recipe was one of those times–and I disregarded it and baked a second time anyway). I have mostly heard that mandel means almond, but I have heard others say just nut. Brot is bread. Much like Italian biscotti, when mandelbrot entered America the flavoring got sweeter and more chocolatey, and nuts became less mandatory. Unlike biscotti, I think mandelbrot have always been made with some oil (but I am not certain of this). Butter is not so traditional, although it is used in this recipe.
I have had plenty of incredibly tasty mandelbrot flavored similarly to a chocolate chip cookie. This recipe caught my eye, however, because it calls for a fair amount of lemon juice (not zest), lending the cookies a faintly sour note under the sweet. Kind of like baking with buttermilk. The tang is subtle–no one asked about it after eating them, but when I told them it was there they could tell something was pleasantly different from what they expected in the cookie. The only real changes I made were to bake the cookies twice, sprinkle the tops with coarse sugar, and I used mini chocolate chips and cacao nibs instead of regular chocolate chips and chopped nuts.
- Tangy Chocolate Chip Mandelbrot
- Closely adapted from Gale Gand’s butter flour sugar eggs
- 8 T (1 stick, 1/2 cup) unsalted butter, softened
- 1 1/4 cups sugar
- 2 T vegetable oil
- 4 large eggs
- 1/2 cup lemon juice
- 1 T vanilla
- 5 1/4 cups (687 g) AP flour
- 1/2 t baking soda
- 2 t baking powder
- 1/2 t salt
- 2 1/2 cups miniature semisweet chocolate chips
- 1/2 cup cacao nibs
Preheat the oven to 350 F. Prepare a baking sheet by either buttering it, or lining it with silicone or parchment (I used silicone).
Whisk together the flour, baking soda, baking powder and salt. Set aside.
Cream the butter until light and fluffy. And the sugar and beat until smooth, then add the oil and beat until smooth. Add the eggs one at a time, beating well after each addition. Be sure to scrape down the sides and bottom of bowl as needed. Beat in the vanilla and lemon juice.
Add the flour mixture to the butter mixture–work slows, incorporating the flour in increments, not all at once. Do not over mix. After the last addition, before it has been completely incorporated, add the chocolate chips. Mix the entire dough just until all chocolate chips and streaks of flour have been evenly incorporated.
Divide the dough into 5 roughly equal portions. Using wet hands, shape into 5 logs on the prepared cookie sheet, lying horizontally, about 1 1/2 inches in diameter. Space the logs as far apart as you can.
Bake for 25-30 minutes, until the logs have become light golden brown. Let cool for at least 1 hour, and then slice into 3/4 inch slices. Turn the oven on to 300 F. Spread the slices on 2 cookie sheets and return them to the oven. Toast for another 20-30 minutes. Cool cookies completely before storing.