The Koch snowflake is a fractal curve. In fact, it's one of the earliest fractals ever described.
The snowflake is constructed from three Koch curves. With each iteration (which you can initiate with a click or a tap), each segment is replaced with four segments, each of them one third the original curve's length, forming a snowflake pattern.
The remarkable thing about the Koch snowflake is that, with each iteration, the perimeter increases by one third. As you iterate, the perimeter increases without limit. As you approach the true fractal, the perimeter increases to infinity, while the area it bounds approaches only eight fifths of the original area.
Note: to avoid your browser catching fire, this one isn't actually infinite.
Code