This Demonstration illustrates the simplest multifractal: Mandelbrot's binomial measure on the interval . The iteration begins with a uniform distribution (with ), subdivides it into a distribution with and , further subdivides it into , , , and , and so on. Additional iteration of this procedure gives a multiplicative cascade that generates an infinite sequence of measures; the limit of the measures is the binomial measure.

B. B. Mandelbrot, "Intermittent Turbulence in Self Similar Cascades: Divergences of High Moments and Dimension of the Carrier," Journal of Fluid Mechanics, 62, 1974 pp. 331–365.