In the mid-1980s, like Walkman cassette players and tie-dyed shirts, the buglike silhouette of the Mandelbrot set was everywhere.<\/p>\n

Students plastered it to dorm room walls around the world. Mathematicians received hundreds of letters, eager requests for printouts of the set. (In response, some of them produced catalogs, complete with price lists; others compiled its most striking features into books.) More tech-savvy fans could turn to the August 1985 issue of Scientific American<\/em>. On its cover, the Mandelbrot set unfolded in fiery tendrils, its border aflame; inside were careful programming instructions, detailing how readers might generate the iconic image for themselves.<\/p>\n

By then, those tendrils had also extended their reach far beyond mathematics, into seemingly unrelated corners of everyday life. Within the next few years, the Mandelbrot set would inspire David Hockney\u2019s newest paintings and several musicians\u2019 newest compositions \u2014 fuguelike pieces in the style of Bach. It would appear in the pages of John Updike\u2019s fiction, and guide how the literary critic Hugh Kenner analyzed the poetry of Ezra Pound. It would become the subject of psychedelic hallucinations, and of a popular documentary narrated by the sci-fi great Arthur C. Clarke.<\/p>\n

The Mandelbrot set is a special shape, with a fractal outline. Use a computer to zoom in on the set\u2019s jagged boundary, and you\u2019ll encounter valleys of seahorses and parades of elephants, spiral galaxies and neuron-like filaments. No matter how deep you explore, you\u2019ll always see near-copies of the original set \u2014 an infinite, dizzying cascade of self-similarity.<\/p>\n

That self-similarity was a core element of James Gleick\u2019s bestselling book Chaos<\/em>, which cemented the Mandelbrot set\u2019s place in popular culture. \u201cIt held a universe of ideas,\u201d Gleick wrote. \u201cA modern philosophy of art, a justification of the new role of experimentation in mathematics, a way of bringing complex systems before a large public.\u201d<\/p>\n