What is the Sierpinski triangle?

Answer 1

The Sierpinski triangle is a fractal (named after Waclaw Sierpinski).

The base state for this fractal is a single triangle. Pick one of the vertices on the triangle and define that vertex as "pointing up" (this helps when describing the fractal without pictures).

Upon each iteration, take each triangle which is pointing up and inscribe an inverted triangle inside of it. The new triangle should have one vertex at the midpoint of each of the sides of the triangle it is in. This will effectively divide the original triangle into four equally sized triangles, three of which are oriented the same way as the original (they point up), and one of which is inverted (points down).

See the related links section for a graphical view of this fractal, as well as detail about the math behind it.