A fractal is an infinite repeating pattern made up of copies (or slight variations) of the same shape. In this picture, the green branch is (essentially) the same shape as the entire picture.
State transparency means putting everything back exactly as it was when you started. It is especially important when blocks depend on other blocks. Usually, this means returning the sprite to the same position and direction and returning the pen to the same color and size.
Using a procedure inside of itself is called recursion.
This different version for the lowest level of a recursive script is called the base case.