…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.…