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arXiv · 2402.17765

On an abrasion motivated fractal model

Balázs Bárány·Gábor Domokos·Ágoston Szesztay
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Abstract

In this paper, we consider a fractal model motivated by the abrasion of convex polyhedra, where the abrasion is realised by chipping small neighbourhoods of vertices. After providing a formal description of the successive chippings, we show that the net of edges converge to a compact limit set under mild assumptions. Furthermore, we study the upper box-counting dimension and the Hausdorff dimension of the limiting object of the net of edges after infinitely many chipping.

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Balázs Bárány, Gábor Domokos, Ágoston Szesztay. 2024-02-27. On an abrasion motivated fractal model. https://arxiv.org/abs/2402.17765

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