I want a list of open conjectures on fractals.
Preferably easy to understand and low dimensions.
Before you say Eremenko's conjecture ( https://en.wikipedia.org/wiki/Escaping_set ):
https://arxiv.org/pdf/2108.10256.pdf
claims a counterexample.
2026-03-29 07:38:56.1774769936
List of open conjectures on fractals
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The MLC conjecture: the Mandelbrot set is locally connected. See here for the statement and here for discussion of its significance. For a popular discussion, see here.
This paper relates MLC to other conjectures, stated as the Density of Hyperbolicity Conjecture, the Rigidity Conjecture, the No Invariant Line Fields Conjecture, and the Triviality of Fibers Conjecture.