Fig. 3

Recipes broken down by complexity, showing why crossovers happen. On the right is a big kitchen with 381 ingredients. On the left is a small kitchen with one-third as many ingredients. In the big kitchen b, we can make a total of 56,498 recipes. Each bar counts recipes with the same number of ingredients (complexity). When we move to the smaller kitchen a, the number of makeable recipes shrinks dramatically to 597, or 1.0%. But this reduction is far from uniform across different bars. Higher bars shrink more, on average by an extra factor of 3 with each bar. Thus, the number of recipes of complexity one (first bar) shrinks about threefold; the number of complexity two (second bar) ninefold, and so on. Of all the recipes in the big kitchen, 4801 contain cocoa d and 7950 contain cayenne f. The cayenne recipes tend to be more complex, containing on average 10.6 ingredients, whereas the cocoa recipes are simpler, averaging 7.2 ingredients. Because higher bars suffer stronger reduction, overall fewer cayenne recipes (0.5%) survive in the smaller kitchen e than cocoa recipes (1.8%) c. Thus, cayenne is more useful in the big kitchen, but cocoa is more useful in the small kitchen