Skirt length oscillations
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…and other applications of non-linear dynamics. A press release from Northwestern University — "Bell-bottoms today, miniskirts tomorrow: Math reveals fashion's 20-year cycle":
Fashion insiders and beauty magazines have long cited the "20-year-rule"—the idea that clothing trends often resurface every two decades. According to Northwestern University scientists, that observation isn't just anecdotal. It's a mathematical reality.
In a new study, the Northwestern team developed a new mathematical model showing that fashion trends tend to cycle roughly every 20 years. By analyzing roughly 37,000 images of women's clothing spanning from 1869 to today, the team found that styles rise in popularity, fall out of favor and then eventually experience renewal. Along with supporting common perceptions about the life cycles of fads, the researchers say these results could help explain how new ideas spread in society.
The study's lead author, Emma Zajdela, will present these findings on Tuesday, March 17, at the American Physical Society (APS) Global Physics Summit in Denver. Her talk, "Back in Fashion: Modeling the Cyclical Dynamics of Trends," is part of the session "Statistical Physics of Networks and Complex Society Systems."
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 and time-delay dynamics. 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.
In fashion (as in music, birdsong, and language), maximal appeal comes from the introduction of modest innovation into familiar patterns.
Zajdela's 2023 PhD dissertation — "Mathematical modeling of complex systems with applications to scientific collaboration at conferences and chimera states for coupled oscillators":
Complex systems exhibit the remarkable property that the behavior of the collective is greater than the sum of its parts. Mathematical modeling validated with data provides understanding of the underlying mechanisms that drive these emergent behaviors. Here, we present models of two types of complex systems using an applied dynamical systems framework: a social system and a system of coupled oscillators. The first model predicts how scientific collaborations form at in-person and virtual conferences. The second analyzes coupled oscillators with amplitude and proves the existence and stability of a new class of chimera states, the “phase chimera.”
And an application to conference dynamics — Zajdela, Emma R., Kimberly Huynh, Andrew L. Feig, Richard J. Wiener, and Daniel M. Abrams. "Face-to-face or face-to-screen: A quantitative comparison of conferences modalities." PNAS nexus 4, no. 1 (2025):
The COVID-19 pandemic forced a societal shift from in-person to virtual activities, including scientific conferences. As society navigates a “new normal,” the question arises as to the advantages and disadvantages of these alternative modalities. We introduce two new comprehensive datasets enabling direct comparison between virtual and in-person conferences: the first, from a series of nine small conferences, encompasses over 12,000 pairs of potential scientific collaborators across five virtual and four in-person meetings on a range of scientific topics; the expressed goal of these conferences is to create novel collaborations. The second dataset, from a series of three large physics conferences, encompasses >250,000 possible pairs of scientific collaborators. Our study provides quantitative insight into benefits and drawbacks of virtual and in-person conferences for team formation, community building, and engagement. We demonstrate the causal role of formal interaction on team formation across both modalities. Our findings show that formal interaction impacted team formation significantly more in virtual settings, while informal interaction played a larger role at in-person conferences as compared with virtual. We show that a nonlinear memory model for predicting team formation based on interaction outperforms seven alternative models. The model suggests that prior knowledge and interaction time contribute to catalyzing collaborations in both settings. Our results underscore the critical responsibility of organizers for optimizing professional interactions, whether virtual or in-person.
AntC said,
March 25, 2026 @ 6:03 pm
So fashion cycles align with Hale's Law?
Barbara Phillips Long said,
March 25, 2026 @ 11:30 pm
The series of fashion illustrations above starts after World War I. The oscillation in hemlines would look much different for hemlines from, say, 1600 to 1900. I would like to know how far back the oscillation pattern holds. My impression is that fashion cycles were much longer before WWI, although they may have accelerated in the 1800s. Style oscillation may have involved skirt width, waist location, sleeve styles, or other factors instead of hemlines. (What I did find interesting is how the oscillation accounts for longer women's hemlines in the 1950s, which is conventionally attributed to the greater availability of cloth after World War II ended.) Color preference oscillations may have been more affected by improvements in dyes, particularly in the 1800s. These days color cycles in U.S. fashion are influenced by corporate interests (such as Pantene) in addition to customer taste.
Men's suit styles may not fit into the 20-year oscillation. The black-and-white formal suit that Beau Brummel advocated during the English Regency period, which was a huge contrast to the very colorful male clothing of the well-to-do in Georgian England, has remained a standard for men's formal attire. Suit styles for men have changed over time, but not as much as dress styles for women. Do variations such as single-breasted vs. double-breasted suit jackets, lapel widths, or suit jacket vent patterns follow a regular oscillation pattern?
Philip Taylor said,
March 26, 2026 @ 4:19 am
The BBC covered this almost ten days ago — https://www.sciencefocus.com/news/major-fashion-rule-mathematically-true-20-years
Philip Taylor said,
March 26, 2026 @ 5:15 am
"These days color cycles in U.S. fashion are influenced by corporate interests (such as Pantene)" —I assume that despite your reference to "color", it was indeed Pantene of whom you are thinking and not Pantone ?
Kate Bunting said,
March 26, 2026 @ 6:05 am
My first thought was exactly the same as Barbara's. Of course, before 1900 women's skirts were always more or less full-length; waistlines for both sexes varied, but on a much longer cycle. 18th century portraits of men dressed up in 'Cavalier' costume are usually easy to spot because the waists are much lower than in real mid-17th century clothing, in accordance with what looked 'right' to the Georgians.
David Marjanović said,
March 26, 2026 @ 10:20 am
Bell-bottoms did come back, but only for women.
Today's miniskirts are mostly fake – they're shorts with an extra loincloth on top, immune to wardrobe malfunctions.
cervantes said,
March 26, 2026 @ 11:50 am
It seems to me that in modern times at least "fashion" is created by the clothing industry. It isn't a phenomenon created by some sort of mass-based social process. The designers decide what is going to be "in" this year. They change it regularly so that people will buy new clothing even if some of their old stuff is still good.
Chester Draws said,
March 26, 2026 @ 1:52 pm
Cervantes: you can only work with willing customers. Fashion exists because people want it to exist. No-one forces people to buy magazines such as Vogue.
There's tons of examples of industry trying to create fashions and failing miserably.
Hats used to be a considerable industry. Now, caps aside, they are barely worn. I would bet that the hat industry spent considerably when they started to go out of fashion, but it didn't work.
What is different these days is the extent of fashion's reach. It used to be those with money, but now twelve year old boys have very strong opinions of what shoes are acceptable, for example, and considerable numbers of them.
Michael Vnuk said,
March 26, 2026 @ 3:46 pm
Oscar Wilde said 'Fashion is a form of ugliness so intolerable that we have to alter it every six months.'
Barbara Phillips Long said,
March 26, 2026 @ 6:23 pm
@ Philip Taylor —
Thanks for catching that typo. It is indeed Pantone, not the hair-care product company Pantene.
Philip Taylor said,
March 27, 2026 @ 6:52 am
Ah, a shame — I had really hoped that you meant "Pantene" because their 2008 commercial featuring a young deaf girl mastering the violin against all odds [*] still moves me to tears to this day.
[*] https://www.youtube.com/watch?v=Ect56804xfA
Tom said,
March 27, 2026 @ 9:07 am
Obviously, this analysis can only work on persistent aspects of clothing such as hem length. Powdered wigs aren't going in and out, and neither are (permanent) tattoos.
Also, more and more, manufacturing methods and costs are driving styles. In the last few years white soles have become ubiquitious, even on brown leather formal/business shoes. I'm pretty sure this has more to do with the ease of having universal soles than how they actually look. Wide lapels are never coming back because they require more fabric to prosuce. Take a look at UNIQLO. It's clothes are all boxy because straight lines are easier and cheaper to sew. How aboit leggings and yoga pants? There's nowhere for this trend to go, which is why Lulu Lemon has been maxing profit by decreasing quality.
A few years back, I had ESL students who working on full body scanners to be used in "automated bespoke" tailoring. This was a great idea, but it was never going to cost friendly.
Philip Taylor said,
March 27, 2026 @ 11:30 am
"In the last few years white soles have become ubiquitous" — in which countries, Tom ?
Olaf Zimmermann said,
March 27, 2026 @ 1:54 pm
Quoth Pilip Taylor ""In the last few years white soles have become ubiquitous" — in which countries, Tom ?
Mid '90s we had all these USAmerican tourists on our planes – a stewardess said to me "makes you feel as if you were on a charter flight". Those were the days. (I guess the USD is overvalued yet again.)