The Mathematics of Monkeybread

New video about Monkeybread! Secretly part of the Scutoid series, but mostly about Voronoi diagrams, and a little bit about the mathematical features of the Bundt pan. Hopefully you’ll never see baked goods in the same way again.

I wrote a little bit about the process here:


So say you’re ruining yet another batch of cookies because, who knows, too much butter? Not enough flour? Didn’t chill the dough long enough? Could be anything, there’s too many variables and this is why baking from scratch is hard and I’ll stick with mathematics thank you very much.

But I do know one delicious recipe that’s hard to get wrong. And by the way this video is in VR180 so use a headset or look around by moving your phone or dragging the video because today we’re making Monkeybread.

Monkeybread, aka puzzle bread or pull-apart bread, is a classic american food invented in the 1970s to take advantage of pre-prepared refrigerated biscuit dough for an easy-to-make snack suitable for groups of children and/or adults with no plates or utensils necessary.

I’ll be making the dough bits round to better simulate properties of Voronoi diagrams, but the basic idea is that each ball of dough is like a little cell coated in cinnamon sugar, and large amounts of brown sugar butter. Lots and lots of butter.

In the oven all these spheres of dough will expand and develop facets as they smoosh into each other, so they’re more polygonal and no longer spheres. What kind of shapes would you expect the cells to form? 

Let’s go back to my batch of cookie, and I’ll use icing to draw the lines where the cookieblobs hit each other. It looks a lot like a Voronoi diagram, which is a kind of diagram where you start with a bunch of points, or, cookiedough blobs, and then it’s as if each point spreads out until it gets all the area that’s close to it, or at least, closer to it than to any other point.

If you started with points organized into a very efficient cookie packing like this, then the Voronoi diagram would look like a bunch of hexagons, except on the edges where technically the cell includes the slice of space going infinitely off the cookie sheet, not that I have enough dough for infinitely large cookies, which just marks another place where mathematical theory is better than the realities of baking.

But for our more randomly placed cookie blob sheet, the Voronoi cells are irregular polygons, and these look pretty typical for 2D Voronoi cells.

But what about 3D Voronoi cells?

There’s many theoretically perfect way to pack spheres together where they’d expand into perfectly fitting cubes or rhombic dodecahedra or other fun shapes, but when you toss all the dough balls randomly into a bundt pan we’ll get more typical random Voronoi cells. I mean it’s not quite mathematically Voronoi-y because of how dough works and physics but it’s similar enough that our Monkeybread bits will have that distinctive Voronoi flavor.

The Bundt pan, by the way, not only makes genus 0 baked goods into genus 1 baked goods, but the hole in the middle adds surface area, which is not only great for having lots of glaze or crust but essential for Monkeybread in particular so that more cells are on the surface. You eat it by just grabbing a cell and pulling it apart from the bread, and the toroidal shape means you can pick at it from all sides, including inside.

Bundt pans also provide areas of both negative and positive curvature to observe, which helps better simulate a comparison to the formation of epithelial cells, hence the Scutoid connection (more about scutoids next time).

Altogether, Monkeybread is quite the mathematical snack.

Vi Hart