The growth of filamentous organisms can be simulated using a deterministic context free grammar, also known as a parallel string rewriting 'L'-System. The following example is a simulation of algae growth, starting with an initial string (called the 'axiom') of 4 and using twelve grammar rules (see table) which are applied to all corresponding symbols at each step (or generation). The various digits represent different life stages and the parentheses represent subbranching.
| Axiom | 4 |
|---|
| Grammar Rules | 0 => 1 0 | 2 => 3 ( 4 ) | 4 => 5 6 | 6 => 5 8 | 8 => 5 0 | ( => ( |
|---|---|---|---|---|---|---|
| 1 => 3 2 | 3 => 3 | 5 => 3 7 | 7 => 3 ( 9 ) | 9 => 3 9 | ) => ) |
Here are the character strings resulting from the first twelve generations (starting with the axiom, with the various digits representing the different life stages and parentheses designating subbranching):
| Step | String |
|---|---|
| 1 | 4 |
| 2 | 56 |
| 3 | 3758 |
| 4 | 33(9)3750 |
| 5 | 33(39)33(9)3710 |
| 6 | 33(339)33(39)33(9)3210 |
| 7 | 33(3339)33(339)33(39)33(4)3210 |
| 8 | 33(33339)33(3339)33(339)33(56)33(4)3210 |
| 9 | 33(333339)33(33339)33(3339)33(3758)33(56)33(4)3210 |
| 10 | 33(3333339)33(333339)33(33339)33(33(9)3750)33(3758)33(56)33(4)3210 |
| 11 | 33(33333339)33(3333339)33(333339)33(33(39)33(9)3710)33(33(9)3750)33(3758 |
| 12 | 33(333333339)33(33333339)33(3333339)33(33(339)33(39)33(9)3210)33(33(39)3 |
Here is the animated simulation resulting from the first twelve generations (with the various colors representing the different life stage symbols):
| Reload to repeat animation |