A Generalization of the Hausdorff Dimension Theorem for Fractals
Dynamical Systems
2022-06-07 v8
Abstract
How many fractals exist in nature or the virtual world In this work, we partially answer the second question using Mandelbrots fundamental definition of fractals and their quantities of the Hausdorff dimension and Lebesgue measure. We prove the existence of beth-two of virtual fractals with a Hausdorff dimension of a bivariate function of them and the given Lebesgue measure. The question remains unanswered for other fractal dimensions.
Cite
@article{arxiv.2007.07991,
title = {A Generalization of the Hausdorff Dimension Theorem for Fractals},
author = {Mohsen Soltanifar},
journal= {arXiv preprint arXiv:2007.07991},
year = {2022}
}
Comments
10 pages