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arXiv · 2201.02552

The Persistence Landscapes of Affine Fractals

Michael J. Catanzaro·Lee Przybylski·Eric S. Weber
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Abstract

We develop a method for calculating the persistence landscapes of affine fractals using the parameters of the corresponding transformations. Given an iterated function system of affine transformations that satisfies a certain compatibility condition, we prove that there exists an affine transformation acting on the space of persistence landscapes which intertwines the action of the iterated function system. This latter affine transformation is a strict contraction and its unique fixed point is the persistence landscape of the affine fractal. We present several examples of the theory as well as confirm the main results through simulations.

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BibTeXRIS

Michael J. Catanzaro, Lee Przybylski, Eric S. Weber. 2022-01-07. The Persistence Landscapes of Affine Fractals. https://arxiv.org/abs/2201.02552

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