Fermat Primes and Pascal’s Triangle

If you take the entries Pascal’s triangle mod 2 and draw black for 1 and white for 0, you get a pleasing pattern:

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The th row consists of all 1’s. If you look at the triangle consisting of the first rows, and take the limit as you get a fractal called the Sierpinski gasket. This can also be formed by repeatedly cutting triangular holes out of an equilateral triangle:

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Something nice happens if you interpret the rows of Pascal’s triangle mod 2 as numbers written in binary:

1 = 1
11 = 3
101...