Benoit B. Mandelbrot (1924–2010) was the Polish-born French mathematician who invented a branch of mathematics called fractal geometry, which is designed to find order in apparently erratic shapes and processes. As a pioneer of chaos theory, he developed and found applications for fractal geometry—and all this as a largely self-taught mathematician who did not like pure logical analysis. Unlike traditional geometry with its regular shapes and whole-number dimensions, fractal geometry uses shapes found in nature with non-integer (or fractal, thus the name) dimensions. For example, twigs, tree branches, river systems, and shorelines can be examined using fractals. Today, fractals are often applied not only to the natural world, but to the chemical industry, computer graphics, and even the stock market.