L-Systems

Bracketed L-Systems

To generate branching patterns, Lindenmayer added another feature, the stack, a list of positions and directions, and two more symbols, [ and ], to the alphabet.

The symbol [ means to put the current position and direction at the top of the stack.

The symbol ] means to move the current position and direction to the top entry of the stack, and remove that entry from the stack.

As an example, we construct a geometric realization of the string

F[+F[+F]F][-F[-F]F]F[+F][-F]

taking q = 30 deg.

To illustrate the making of realisitc images of plants, here are the first, second, and fourth iterates of the L-System with axiom = F and production rule F -> FF-[-F+F+F]+[+F-F-F] (all other symbols are replaced by themselves) taking q = 22 deg.

Exercise For the L-system with axiom F and production rule F -> FF[+F][-F], write the string resulting from one application of the production rule to the axiom, and write the string resulting from two applications of the production rule to the axiom. Taking q = 90 deg, draw geometric realizations of these strings. If you feel especially ambitious, try the next step. Here are the answers.

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