A good book evokes a variety of emotions as you read. Turns out, though, that almost all novels and plays provide one of only six “emotional experiences” from beginning to end—a rags-to-riches exuberance, say, or a rise and fall of hope (below, top). Researchers at the University of Vermont graphed the happiness and sadness of words that occurred across the pages of more than 1,300 fiction works to reveal the emotional arcs and discovered relatively few variations.

A different study coordinated by Poland's Institute of Nuclear Physics found that sentence lengths in books frequently form a fractal pattern—a set of objects that repeat on a small and large scale, the way small, triangular leaflets make up larger, triangular leaves that make up a larger, triangular palm frond (below, bottom).

Why analyze the mathematics of literature? Vermont applied mathematician Andrew J. Reagan notes that “tons of data” from the Human Genome Project “taught us so much more about genes than we knew before. Maybe data can teach us more about stories, too.”

Credit: Andrew J. Reagan (emotional arcs) and Jen Christiansen (fractal charts); Sources: “The Emotional Arcs of Stories Are Dominated by Six Basic Shapes,” by Andrew J. Reagan et al., in EPJ Data Science, Vol. 5, No. 1, Article No. 31; December 2016 (arcs); “Quantifying Origin and Character of Long-Range Correlations in Narrative Texts,” by Stanislaw Drozdz et al., in Information Sciences, Vol. 331; February 20, 2016 (fractals)