Cantor tree surface

Short description: Fractal with infinite genus

The bark of a fractal tree, splitting in two directions at each branch point, forms a Cantor tree surface. Drilling a hole through the tree at each branch point would produce a blooming Cantor tree. An Alexander horned sphere. Its non-singular points form a Cantor tree surface.

In dynamical systems, the Cantor tree is an infinite-genus surface homeomorphic to a sphere with a Cantor set removed. The blooming Cantor tree is a Cantor tree with an infinite number of handles added in such a way that every end is a limit of handles.[1][2]

## See also

* Jacob's ladder surface
* Loch Ness monster surface

## References

1. ↑ Ghys, Étienne (1995), "Topologie des feuilles génériques" (in fr), Annals of Mathematics, Second Series 141 (2): 387–422, doi:10.2307/2118526, ISSN 0003-486X
2. ↑ Walczak, Paweł (2004), Dynamics of foliations, groups and pseudogroups, Instytut Matematyczny Polskiej Akademii Nauk. Monografie Matematyczne (New Series) [Mathematics Institute of the Polish Academy of Sciences. Mathematical Monographs (New Series)], 64, Birkhäuser Verlag, p. 210, ISBN 978-3-7643-7091-6, https://books.google.com/books?id=Tl4WkcHzhIAC

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