artificial life

Chapter 4: Lindenmayer Systems

4.1 Aristid Lindenmayer

Aristid Lindenmayer, a biologist in the 1960’s, was interested in modeling the growth pattern of a type of algae using a grammar. He noted that the algae had two different states, a and b. If a cell of algae was in state b it grew into a cell of state a. The cells in state a divided into two cells, one in state a and the other in state b. Lindenmayer proposed a grammar system that took an initial string and rewrote it using a set of rules.

An L-System for his algae is described as follows:

Rule 1: a in the current string becomes ab in the next step

Rule 2: b in the current string becomes b in the next step

Initial string “a”:

Iteration 1: a -> ab

Iteration 2: ab -> aba

Iteration 3: aba -> abaab

Iteration 4: abaab -> abaababa

Lindenmayer was able to confirm his prediction by comparing the grammars his system produced with algae under a microscope. The idea of a rewriting grammar turned out to be very powerful in terms of a-life. Lindenmayer barely scratched the surface when he used them to describe the growth of algae [Prusinkiewicz, et al, 1989].