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Cantor tree surface information


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]

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  2. ^ Cite error: The named reference walczak was invoked but never defined (see the help page).

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Cantor tree surface

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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...

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List of surfaces

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Whitney umbrella Boy's surface Cantor tree surface Homoeoid Jacob's ladder surface Loch Ness monster surface Morin surface Seashell surface Superegg Supertoroid...

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List of things named after Georg Cantor

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function Cantor set Cantor space Cantor tree surface Cantor's back-and-forth method Cantor's diagonal argument Cantor's intersection theorem Cantor's isomorphism...

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Alexander horned sphere

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Antoine's necklace, a pathological embedding of the Cantor set into the 3-sphere. Cantor tree surface List of topologies Platonic solid Wild arc, specifically...

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Loch Ness monster surface

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the surface of Loch Ness) and adding an infinite number of handles (which can be thought of as loops of the Loch Ness monster). Cantor tree surface Jacob's...

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Fractal

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Saturn River networks Romanesco broccoli Snowflakes Soil pores Surfaces in turbulent flows Trees Frost crystals occurring naturally on cold glass form fractal...

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List of mathematical shapes

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Apollonian gasket Apollonian sphere packing Blancmange curve Cantor dust Cantor set Cantor tesseract[citation needed] Circle inversion fractal De Rham...

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Menger sponge

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curve. It is a three-dimensional generalization of the one-dimensional Cantor set and two-dimensional Sierpinski carpet. It was first described by Karl...

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Asian giant softshell turtle

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Asian giant softshell turtle (Pelochelys cantorii), also known commonly as Cantor's giant softshell turtle and the frog-faced softshell turtle, is a species...

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List of Alfred Hitchcock Presents episodes

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Charlie Cantor as Barney, Shirley Smith as Goldie, Harry Tyler as Timmy, Herb Vigran as Newsman, Lee Erickson as Messenger Boy Note: Charlie Cantor and Herb...

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Chinese cobra

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described by Danish physician, zoologist, and botanist Theodore Edward Cantor in 1842. The generic name naja is a Latinisation of the Sanskrit word nāgá...

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Patterns in nature

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species of tree has its own structure at the levels of cell and of molecules, each has its own pattern of splitting in its bark. Old pottery surface, white...

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Latrodectus

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1837 – USA, Canada Nomina dubia L. dotatus C. L. Koch, 1841 L. limacidus Cantor, 1842 L. pallidus Caporiacco, 1933 Widow spiders are found on every continent...

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Sibynophis sagittarius

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Sibynophis sagittarius, commonly known as Cantor's black-headed snake after Theodore Cantor, is a species of snake endemic to South Asia. It is found...

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Monocled cobra

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under the trinomial Naja tripudians var. fasciata. In 1839, Theodore Edward Cantor described a brownish monocled cobra with numerous faint yellow transverse...

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List of fractals by Hausdorff dimension

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I.; Balasoiu, M.; Osipov, V.A. (2010). "The scattering from generalized Cantor fractals". J. Appl. Crystallogr. 43 (4): 790–7. arXiv:0911.2497. doi:10...

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List of algorithms

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Procedure for generating cosets. Buchberger's algorithm: finds a Gröbner basis Cantor–Zassenhaus algorithm: factor polynomials over finite fields Faugère F4 algorithm:...

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Mahjong

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during the Mahjong fad, most notably "Since Ma Is Playing Mah Jong" by Eddie Cantor. Many variants of Mahjong developed during this period. By the 1930s, many...

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Tiger tail seahorse

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in the family Syngnathidae. The species was first described by Theodore Cantor in 1850. It is found in India, Indonesia, Malaysia, the Philippines, Singapore...

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Channa

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Channa andrao Britz, 2013 Channa ara (Deraniyagala, 1945) Channa argus (Cantor, 1842) (northern snakehead) Channa aristonei Praveenraj, Thackeray, Singh...

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Vairocana

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Vairocana, made in China during the Ming dynasty (1368–1644). Displayed at the Cantor Center for Visual Arts. Ming dynasty bronze statue of Vairocana. Displayed...

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Jefferson nickel

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Expedition. They contacted the office of Representative Eric Cantor (Republican-Virginia). Cantor had concerns about moving Monticello, located in his home...

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Himalayas

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Ethnomedicine. 9: 1. doi:10.1186/1746-4269-9-1. PMC 3560114. PMID 23281594. Cantor, Kimberly (14 July 2016). "Paro, Bhutan: The Tiger's Nest". Huffington Post...

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Pond loach

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& Bray, D.J. (2020). Oriental Weatherloach, Misgurnus anguillicaudatus (Cantor 1842), Fishes of Australia, Museums Victoria. Retrieved 2 February 2023...

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Sperm whale

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National Academy of Sciences. 5 December 2022. Retrieved 7 February 2024. Cantor, Maurício; Whitehead, Hal (October 2015). "How does social behavior differ...

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