A fractal dimension is an index for characterizing fractal patterns or sets by quantifying their complexity as a ratio of the change in detail to the change in scale. Several types of fractal dimension can be measured theoretically and empirically (see Fig. 2). Fractal dimensions are used to characterize a broad spectrum of objects ranging from the abstract to practical phenomena, including turbulence, river networks, urban growth, human physiology, medicine, and market trends. The essential idea of "fractional" or "fractal" dimensions has a long history in mathematics that can be traced back to the 1600s, but the terms "fractal" and "fractal dimension" were coined by mathematician Benoit Mandelbrot in 1975.