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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  Animated construction. Click to enlarge.

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  Sierpinski triangle evolution square

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  Animated creation of a Sierpiński triangle using the chaos game

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  Arrowhead construction of the Sierpiński gasket

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  A level-5 approximation to a Sierpiński triangle obtained by shading the first 25 (32) levels of a Pascal's triangle white if the binomial coefficient is even and black otherwise

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  Sierpiński pyramid recursion (8 steps)