Sierpinski triangle fractal

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The Sierpinski Triangle is a fractal named after a Polish mathematician named Wacław Sierpinski, who is best known for his work in an area of math called set theory. Here’s how it works.

We start with an equilateral triangle, which is one where all three sides are the same length:

Now we repeat the following rule on this triangle indefinitely:

The Rule: Whenever you see an equilateral triangle, like the one below on the left, chop it up into four little equilateral triangles, and get rid of the middle upside-down triangle, so you’re left with the thing on the right.

Now let’s try it for our beginning triangle.

First, we apply The Rule once:

Now for each of those little gray triangles we have left, we’ll apply The Rule again:

And we’re left with more little gray triangles, so we can apply The Rule again:

And we’ll always keep getting smaller and smaller gray triangles, so we can keep doing this for as long