To draw a Koch snowflake, start with an equilateral triangle and then break each line segment into thirds, replacing the middle third with the other two sides of an equilateral triangle pointing out. Repeat this process forever (or until you get bored).
How does the appearance of the Koch snowflake (or, more precisely, an approximation to it of a few iterations) change when the triangle used to replace the missing segment is not equilateral. In one limit the line segment is replaced with a straight line so a single triangle results. In another limit the middle "third" has length 0 and is replaced by a perpendicular spike (which is then split on both sides). This program draws everything in between.