L-Systems were invented in 1968 by Aristid Lindenmayer to model biological growth. They provide a flexible method for drawing many curves and fractals.
They start with an axiom list, and then use a set of production rules to modify the elements in this list. This process of string substitutions is then repeated at each iteration. It can create very long lists.
A second procedure then renders the list, by translating each element into a turtle command which draws the final curve.
Also see Fractals.