Sierpinski Gasket

The Sierpinski Gasket a triangle with the center triangle cut out of each solid triangle recursively. It can be shown that the triangle has no area. This image can be generated in many ways.

• One is to create it out of lines by recursively adding smaller and smaller triangles.
• Another is to remove the triangles recusivly.
• The pattern can also be generated by taking the numbers in Pascal's Triangle and mod-ing them by 2.

This set of patterns was generater by initially starting at the top vertex. A vertex is randomly selected and a new point is drawn midway between the current point and the vertex selected. Another vertex is then picked and a new point is drawn midway between the last point drawn and the new vertex. This process is continued until the Stop button is used.

The method of cutting out the center can be applied to other shapes in 2 and 3 dimensions. The following is an example of a cube with no volume known as the "Menck Sponge". The color is of course meaningless and only four iterations of cutting were done in this example. The real sponge is infinatly recursed.