Pascal's Triange

When I was looking for ideas about Pascal's triangle to write my blog on, the pattern that was most interesting was Sierpinski's triangle. It is formed by coloring odd numbers one color and even numbers another color, like so:

When I saw this pattern, I immediately recognized it as a fractal: a pattern that repeats indefinitely. Here is a picture of Sierpinski's triangle in more detail:

This pattern would repeat indefinitely because when you add two even numbers or two odd numbers together you get an even number, and when you add an even and an odd number together, you get an odd number. Since you get the numbers of Pascal's triangle by adding the two numbers above, this pattern will repeat.

A few years ago, I was a part of the effort to set the world record for the largest Sierpinski's triangle. Now, I am mindblown by the connection to Pascal's triangle. And in case you want to make one of these yourself, all you have to do is draw a triangle, the connect the midpoints of the triangle. Then continue doing this in each of the three outside triangles that you just formed.