Sierpinski triangle

A Sierpinski triangle or Sierpinski triangle gasket is a fractal resulting from doing the following:

• Start with an equilateral triangle.
• Remove center part.
• Do the same for the three largest equilateral triangles left in this one.

If this is done, the first few steps will look like this:

If this is done an infinite number of times, its area will be 0.

They can also be 3D:

Sierpinski Triangle Media

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  Sierpinskitriangle

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  Generated using a random algorithm

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  Sierpiński triangle in logic: The first 16 conjunctions of lexicographically ordered arguments. The columns interpreted as binary numbers give 1, 3, 5, 15, 17, 51... (sequence [{{fullurl:OEIS:{{{id}}}}} {{{id}}}] in OEIS)

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  Sierpiński pyramid as light installation fractal on the Tetrahedron in Bottrop, Germany

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  Sierpinskitriangleevolutionsquare

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  Animated creation of a Sierpinski triangle using the chaos game

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  Animated construction of a Sierpinski triangle

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  A Sierpinski Triangle is outlined by a fractal tree with three branches forming an angle of 120° and splitting off at the midpoints. If the angle is reduced, the triangle can be continuously transformed into a fractal resembling a tree.

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  Each subtriangle of the nth iteration of the deterministic Sierpinski triangle has an address on a tree with n levels (if n=∞ then the tree is also a fractal); T=top/center, L=left, R=right, and these sequences can represent both the deterministic form and, "a series of moves in the chaos game"