Back in Fashion: Modeling the Cyclical Dynamics of Trends

Many people have experienced firsthand the idea that "fashion comes back," from bell-bottom jeans to mini-skirts. Historically, a lack of quantitative data posed a barrier to explicit mathematical study of this system; however, newly digitized historical records now make such work possible. We constructed a new database quantifying tens of thousands of women’s dresses from 1869 to present day. Our analysis indicates that fashion is cyclical and, remarkably, in line with common knowledge in the fashion industry, this cycle is approximately 20 years long. We developed a mathematical model to understand and predict the evolution of these trends inspired by a continuous-time version of bounded confidence interval models for opinion dynamics. This model includes the idea of “optimal distinctiveness,'' which has been shown to be present in other dynamics of human innovation. It also includes time-delay dynamics where trends need to be different from the past to remain fashionable, in line with the idea that “the problem with fashion is that it goes out of fashion,” in the words of designer Agnes B. This conceptually simple mechanistic model performs well at replicating the dynamics of the trends observed. Large-scale social phenomena such as fashion trends are of intrinsic interest themselves, but a better understanding of this fashion system will contribute to elucidating the interplay of creativity, differentiation, conformity, and diffusion of ideas in broader human systems.