The infinite partition of a line segment and multifractal objects

Simple item page
dc.creatorde Araújo, A. I. L.
dc.creatorSoares, R. F.
dc.creatorde Oliveira, J. P.
dc.creatorCorso, G.
dc.date2008-11-07
dc.date.accessioned2026-07-07T10:16:50Z
dc.date.available2026-07-07T10:16:50Z
dc.descriptionWe 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 $2^n$ and the number of elements in a same $k$-set is $C_n^k$. In the limit of an infinite partion this object become a multifractal where each $k$-set originate a fractal. We find the fractal spectrum $D_k$ and calculate where is its maximum. Finally we find the values of $D_k$ for the limits $k/n \to 0$ and 1.
dc.identifierhttps://arxiv.org/abs/0811.1130
dc.identifierhttp://arxiv.org/abs/0811.1130
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/173647
dc.subjectData Analysis, Statistics and Probability
dc.titleThe infinite partition of a line segment and multifractal objects
dc.typetext

Files

Collections

arXiv