One of the most famous integer patterns in the history of mathematics is Pascal's triangle.  Each number in the triangle is the sum of the two above it.  There are countless wonders in the triangle. 

When even numbers in the triangle are replaced by dots and odd numbers by gaps, the resulting pattern is a fractal, with intricate repeating patterns on different scales.   The pattern obtained by coloring only the odd numbers in Pascal's triangle closely resembles the fractal called the Sierpinski triangle. This resemblance becomes more and more accurate as more rows are considered; in the limit, as the number of rows approaches infinity, the resulting pattern is the Sierpinski triangle, assuming a fixed perimeter.