How to Make a Sierpinski Triangle

Last Updated: March 3, 2021

The Sierpinski triangle was named after its inventor, the Polish mathematician Wacław Sierpiński. This intriguing design consists entirely of simple equilateral triangles.

Steps

1
Print out triangular grid paper. You can make your own in a graphics program or print out the image next to this step (click to enlarge)].
2
Draw an equilateral triangle. The sides should each have a number of triangles that is a multiple of four. This example will start with a large triangle that is 16 triangles to a side.
- Don't colour the triangles yet. Just trace the outsides of the ones you will colour.
3
Divide this triangle into four smaller triangles. Leave the one in the middle blank.
4
Divide all the coloured triangles into four smaller triangles just as you did the first one. Again, leave the middle triangle of each set blank.
5
Divide the next smaller coloured triangles into fours, leaving the center of each blank.
6
Divide the next smaller triangles. Colour them as mentioned in the previous steps.
7
Keep dividing triangles as many times as you wish.
8
Finished.

Community Q&A

Question

Are the triangles of each of the Sierpinski triangle similar?

AnonymousSuperWriter

Community Answer

Yes. Although they are the same type of shape, they are not congruent, so they are similar.