# Mandelbrot's Binomial Measure Multifractal

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 [0,1] (with ), subdivides it into a distribution with [0,1/2] and [1/2,1]1-, further subdivides it into [0,1/4], [1/4,1/2], [1/2,3/4], and [3/4,1], 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.

[0,1]

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