The Mandelbrot [man-del-brot] set is a mathematical fractal named after Benoît Mandelbrot, who studied and popularized it. When computed and graphed it displays an elaborate boundary which, being a fractal, does not simplify at any given magnification, meaning it shows more intricate detail the closer one looks or magnifies the image, usually called ‘zooming in.’
The Mandelbrot set has become popular outside mathematics both for its aesthetic appeal and for being a complicated structure arising from a simple definition, and is one of the best-known examples of mathematical visualization. Many mathematicians, including Mandelbrot, communicated this area of mathematics to the public.
The Daily Omnivore 