The bakery project (just a taste)

Meet the recipe tetrahedron, inspired by Ashby plots from the field of materials science. You can print this, cut it out, and fold along the dotted lines to assemble your very own recipe tetrahedron. Boston Globe reporter Carolyn Y. Johnson wrote a great article about this called “The Analyzed Brownie” that comes with a really fun graphic.

The tetrahedron depicts four ingredient dimensions: flour (F), sugar (S), egg (E) and liquid (L). The other primary dimension, missing here, is fat. Each of the four faces of the tetrahedron is a triangle depicting three of these dimensions. As shown in the key, different colors correspond to different kinds of recipes, e.g., brownies are purple and sugar cookies are blue. Each point corresponds to a recipe. A recipe in the center of a triangle has equal ratios by volume of the three ingredients at the corners of the triangle, e.g., a point in the center of the top F-L-S triangle has equal parts flour, liquid, and sugar.

Here are some things to observe:

• For each kind of recipe, there is quite a bit of variance in the ratios of ingredients that people use, e.g., some brownies have less flour and more sugar than other brownies. In other words, the individual recipes are different from one another and correspond to different points in the plots.
• The shaded areas enclose the majority of recipes for each type. For example, the purple shaded areas are drawn around the 80% of the brownie recipes that are closest to the average (mean) brownie recipe. The points that fall outside of these regions are outliers. We can look at the outliers for each distribution and go back to the original recipes to try and understand why they are so different.
• Different kinds of recipes correspond to different clouds of points in different regions of the plots, but these clouds of points aren’t totally distinct. For example, crepes (cyan) tend to have more liquid than pancakes (yellow), but as we can see from the overlap, not all crepes have more liquid than all pancakes. It’s easiest to see this in the top triangle. These plots help us visualize some of the differences between, say, brownies and chocolate cakes.

For more information on using tetrahedra to visualize data, see the Wikipedia page about the simplex.

The data used in this plot was collected by Diana Cai, an undergraduate at Harvard College. This is part of a project with Michael P. Brenner to learn about flour-based baked goods and other foods.