These classic fractals were generated as applications of L-systems, starting with the axiom, using the string replacement rules listed under each corresponding figure, and making turns according to the angle specified. All symbols are replaced simultaneously; those without replacement rules are retained unaltered. The symbols are interpreted as in "Turtle Graphics":
| Symbol | Interpretation |
|---|---|
| F G L R S X Y Z | move and draw line |
| @ | move but don't draw |
| + | turn to the left |
| - | turn to the right |
| [ | begin side branch |
| ] | end side branch |
| Radial snowflake | Sierpinski arrowhead | Sierpinski gasket | Sierpinski curve |
| Koch snowflake | Koch island | Koch mosaic | Koch curve |
| Hilbert curve | Peano S curve | Dragon curve | Gosper curve |