Cantor set: Difference between revisions
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=={{header|Fōrmulæ}}==
{{FormulaeEntry|page=https://formulae.org/?script=examples/
'''Solution'''
Strictly speaking, a visualization of the perfect Cantor set is impossible, it consists of a infinite set of isolated points in the interval [0, 1]. The most we can do is drawing the early steps of its construction.
Several ways of visualization of the Cantor set are shown.
'''Preliminaries'''
Let us start with a definition of the points that define the central points of the intervals of the Cantos set on any step:
[[File:Fōrmulæ - Cantor set 01.png]]
[[File:Fōrmulæ - Cantor set 02.png]]
[[File:Fōrmulæ - Cantor set 03.png]]
The followign function defines the segments on each step:
[[File:Fōrmulæ - Cantor set 04.png]]
[[File:Fōrmulæ - Cantor set 05.png]]
[[File:Fōrmulæ - Cantor set 06.png]]
=== Plotting the central points ===
[[File:Fōrmulæ - Cantor set 07.png]]
[[File:Fōrmulæ - Cantor set 08.png]]
=== Common method ===
[[File:Fōrmulæ - Cantor set 09.png]]
[[File:Fōrmulæ - Cantor set 10.png]]
[[File:Fōrmulæ - Cantor set 11.png]]
=== Cantor dust ===
[[File:Fōrmulæ - Cantor set 12.png]]
[[File:Fōrmulæ - Cantor set 13.png]]
[[File:Fōrmulæ - Cantor set 14.png]]
=== [https://en.wikipedia.org/wiki/Knaster%E2%80%93Kuratowski_fan Knaster–Kuratowski fan or "Cantor teepee"] ===
[[File:Fōrmulæ - Cantor set 15.png]]
[[File:Fōrmulæ - Cantor set 16.png]]
[[File:Fōrmulæ - Cantor set 17.png]]
The following forms of visualization are taken from [https://en.wikipedia.org/wiki/Point-set_topology point-set topology]. They are not intended as forms of visualization of the Cantor set, instead, these structures make use of the Cantor set.
=== [https://en.wikipedia.org/wiki/Indecomposable_continuum Brouwer–Janiszewski–Knaster continuum, or "the bucket handle"] ===
[[File:Fōrmulæ - Cantor set 18.png]]
[[File:Fōrmulæ - Cantor set 19.png]]
[[File:Fōrmulæ - Cantor set 20.png]]
=== "Double Knaster" ===
[[File:Fōrmulæ - Cantor set 21.png]]
[[File:Fōrmulæ - Cantor set 22.png]]
[[File:Fōrmulæ - Cantor set 23.png]]
=={{header|Go}}==
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