Mandelbrot's Binomial Measure Multifractal
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. B. B. Mandelbrot, et al. "A Multifractal Model of Asset Returns". (1997).
S. Seuret and J. L. Véhel, "The Local Hölder Function of a Continuous Function," Computational Harmonic Analysis, 13(3), 2002 pp. 263–276.