In its simplest verison, an L-system consists of
| an alphabet, A, a set of symbols, |
| an axiom S, a string of symbols from the alphabet, and |
| a set P of production rules, rules assign to each letter a of the alphabet a string P(a) of letters of the alphabet. |
The string P(a) is called the successor of a.
Example Suppose the alphabet is
| a -> abc |
| b -> b |
| c -> cba |
One step produces the replacement
a ->abc.
The second step produces
abc ->abc b cba = abcbcba.
(Spaces have been inserted to make clear which parts of the successor come from which parts of the predecessor.) The third step produces
abcbcba -> abc b cba b cba b abc = abcbcbabcbababc,
and so on.
The sequence
a -> abc -> abcbcba -> abcbcbabcbababc -> ...
is called the developmental sequence of the L-System.
Exercise Suppose the alphabet is
(i) If the string abbaab is derived from S in one step, find the production rules. Find the string derived from S in two steps.
(ii) Now suppose the string ababaabab is derived from S in one step. Find two different sets of production rules giving this derivation.
Here are the answers.
Return to L-Systems.