When Benoit Mandelbrot first began the work that led to the birth of fractal geometry, there was "an explosion of interest" from his colleagues. "Everybody in mathematics had given up for 100 years or 200 years the idea that you could...from looking at pictures, find new ideas. That was the case long ago in the Middle Ages, in the Renaissance, in later periods, but by then mathematicians had become very abstract." By contrast, the complex mathematical shapes called fractals were not only available to the senses, they were downright beautiful.
They didn't just turn mathematicians' heads, either, as Mandelbrot recounts in his Big Think interview. Fractals have become beloved by non-mathematicians around the world, to the point of entering the popular culture. There is now not just one but a whole genre of "fractal nightclubs" (he doesn't know what kind of clubs they are, but says he has a guess), as well as a popular rock song named after the most famous fractal of all, the Mandelbrot set.
Mandelbrot admits, however, that while he may have been the first to discover the mathematics behind the rough, self-similar shapes known as fractals, he was by no means the first to notice their prevalence in nature. As he points out, fractals have had a long distinguished history of appearing in the works of great artists, from the French landscape painter Poussin to the Japanese master Hokusai. And as you might expect, modern digital artists are now doing them one better: through the power of fractal equations, for example, computers can now generate clouds so photorealistic, they're indistinguishable from the real thing.