The infinite partition of a line segment and multifractal objects
نویسندگان
چکیده
We report an algorithm for the partition of a line segment according to a given ratio ν. At each step the length distribution among sets of the partition follows a binomial distribution. We call k-set to the set of elements with the same length at the step n. The total number of elements is 2 and the number of elements in a same k-set is C n. In the limit of an infinite partion this object become a multifractal where each k-set originate a fractal. We find the fractal spectrum Dk and calculate where is its maximum. Finally we find the values of Dk for the limits k/n → 0 and 1. keywords: multifractal, binomial distribution, partition of a segment, spectrum of fractal dimensions.
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