Create Alternative Koch Snowflakes

The Koch snowflake is constructed by following a simple rule: put a triangle on top of every line. After this, the picture still consists of lines. To each of these lines, the rule is applied again: put a triangle on top of every line. After applying this refinement infinitely many times, a fractal appears. Three of these fractals put together in a triangle are called the Koch snowflake. In this Demonstration, you can vary the rule for making the snowflake by dragging the points. You can also add points with Alt+click.