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:
Images for kids

Generated using a random algorithm

Animated creation of a Sierpinski triangle using the chaos game

Animated construction of a Sierpinski triangle

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.

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"

Sierpinski triangle using an iterated function system

Animated arrowhead construction of Sierpinski gasket

Arrowhead construction of the Sierpinski gasket

Sierpinski pyramid recursion progression (7 steps)

A Sierpiński trianglebased pyramid as seen from above (4 main sections highlighted). Note the selfsimilarity in this 2dimensional projected view, so that the resulting triangle could be a 2D fractal in itself.
See also
In Spanish: Triángulo de Sierpinski para niños