You will have to paint the same curve in each of the three directions of a triangle. You can do this by writing a function drawKochCurve(double level, double sideLength, double additionalAngle) and calling it three times, adding the additionalAngle.
Wikipedia has more details: The Koch curve originally described by Koch is constructed with only one of the three sides of the original triangle. In other words, three Koch curves make a Koch snowflake. http://en.wikipedia.org/wiki/Koch_snowflake
