In this paper, we use (and extend) this theory to analyze the dimensions of individual points in fractals that are computably self-similar, meaning that they ...
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This paper analyzes the dimensions of points in the most widely known type of fractals, the self-similar fractals. Our analysis uses nontrivial connections ...
We use nontrivial connections between the theory of computing and the fine-scale geometry of Euclidean space to give a complete analysis of the dimensions ...
Jan 27, 2017 · The way we computed the Hausdorff dimension of the self-similar fractals was log(number of smaller copies)/log(linear scale factor).
Jul 3, 2023 · In this paper, we study the effective dimension of points in infinite fractal trees generated recursively by a finite tree over some alphabet.
Dec 27, 2014 · The central square has a size of 12. All subsequent squares have the half of the edge length. The distance is also half of the edge length of ...
We will show how to describe and create these fractals, and how to measure their fractal dimension using the similarity dimension. Strictly Self-Similar ...
We investigate the topological, similarity and Hausdorff dimensions of self-similar fractals that are the invariant sets of iterated function systems. We start ...
May 31, 2023 · Self similarity ensures that the fractal dimension remains unchanged over different scales of magnification.
Calculating Dimensions of Self-Similar Fractals (top). Calculating the fractal dimension of exactly self-similar shapes is fairly straightforward. This ...