Calculus of Variations and Geometric Measure Theory
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T. Lazarus - Q. Xia

Generalized Moran sets Generated by Step-wise Adjustable Iterated Function Systems

created by xia1 on 01 Sep 2021

[BibTeX]

preprint

Inserted: 1 sep 2021

Year: 2017

ArXiv: 1707.08634 PDF

Abstract:

In this article we provide a systematic way of creating generalized Moran sets using an analogous iterated function system (IFS) procedure. We use a step-wise adjustable IFS to introduce some variance (such as non-self-similarity) in the fractal limit sets. The process retains the computational simplicity of a standard IFS procedure. In our construction of the generalized Moran sets, we also weaken the fourth Moran Structure Condition that requires the same pattern of diameter ratios be used across a generation. Moreover, we provide upper and lower bounds for the Hausdorff dimension of the fractals created from this generalized process. Specific examples (Cantor-like sets, Sierpinski-like Triangles, etc) with the calculations of their corresponding dimensions are studied.

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