L-Systems

October 2nd, 2006 by iain | Posted in *, Computing |

An l system is defined by a triplet G = (v,w,P) where:

• v is the alphabet of possible members
• w is the axiom or starting point
• P is a set of productions

The following l-system describes the growth of an algae

• v=(a,b)
• w=a
• P1: a->ab
• P2: b->a

So the sequence develops thus:

• a
• ab
• aba
• abaab
• abaababa
• ……etc……

Flower trigger l-system:

• w: D(1)a(1)
• p1: a(i) : ia(i+1)
• p2: a(i) : i=m->I[L]a(1)
• p3: D(i) : iD(i+1)
• p4: D(i) : i=d->S(1)
• p5: S(i) : iS(i+1)
• p6: S(i) : i=u->e
• p7: S(i)IS(1)
• p8 S(i) I[L]A
• p9: A : * -> K

I is an internode, L are leaves on the main axis (p2). m steps cause a trigger (p1) Then after a delay of d steps (p3) a signal S is sent from the plant base towards the apices (p4). This signal is transported along the main axis with a delay of u steps per internode I (p5,p7). Production p6 removes the signal from a node after it has been transported along the structure (e stands for the empty string). When the signal reaches the apex a is transformed int A, the flowering state (p8) which yields a flower K (p9)

Note that the signal must propogate faster than one node per plastocron (u

From “The algorithmic beauty of plants” Prusinkiewicz and Lindenmayer