Koch Snowflake and Sierpinski Carpet

The Koch Snowflake is obtained fractally by beginning with an equilateral triangle, removing the middle third of each side and replacing it with two sides of a smaller equilateral triangle. This process continues forever (well, considering the limitation of computer pixels, at least for an impressive number of stages).

The Sierpinski Carpet by starting with a square, removing the middle ninth, removing the middle ninth of each remaining square, and continuing.

You can change colors at any time during the construction process.