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arXiv · 2402.00237

Graph Iterated Function Systems and Fractal Tops

Grover Lancaster-Cole·Georgiana Lyall·Thomas Malcolm·Qiyu Zhou
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Abstract

Following the work of Louisa and Michael Barnsley on results in tops of iterated function systems, we extend their work to graph-directed iterated function systems by investigating the relationship between top addresses and shift spaces. For the simplest overlapping interval IFS, we find a sufficient condition for the closure of its tops code space to be a shift space of finite type. Likewise, we find that shift invariance properties do not directly extend to the graph-directed setting.

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Grover Lancaster-Cole, Georgiana Lyall, Thomas Malcolm, Qiyu Zhou. 2024-01-31. Graph Iterated Function Systems and Fractal Tops. https://arxiv.org/abs/2402.00237

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