The Sierpinski's triange we constructed in class! It looks so pretty but it comes from a simple rule: Join the midpoints of the triangle and then shade the new triangle formed.

"The pattern obtained by coloring only the odd numbers in Pascal's triangle closely resembles the fractal called Sierpinski triangle, and 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. "~ Wikipedia

Koch Snowflake! Rule: Divide a line segment into 3, extend a equilatral triangle with the middle line as a base, then erase the middle line.
Animation of the construction of Koch Snowflake (Source: http://en.wikipedia.org/wiki/File:Von_Koch_curve.gif)

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The idea of repeating the same rule again and again to achieve a complex and beautiful structure exemplifies itself in many aspects of nature too.