An L-system or Lindenmayer system is a formal grammar (a set of rules and symbols) most famously used to model the growth processes of plant development, though able to model the morphology of a variety of organisms. L-systems can also be used to generate self-similar fractals such as iterated function systems. L-systems were introduced and developed in 1968 by the Hungarian theoretical biologist and botanist from the University of Utrecht, Aristid Lindenmayer (1925-1989).
Application to generating plant:
As a biologist, Lindenmayer worked with yeast and filamentous fungi and studied the growth patterns of various types of algae, such as the blue/green bacteria Anabaena catenula. Originally the L-systems were devised to provide a formal description of the development of such simple multicellular organisms, and to illustrate the neighbourhood relationships between plant cells. Later on, this system was extended to describe higher plants and complex branching structures.
Source code:
branching.java 
Further reading:
Wikipedia, "L-system", The Web, http://en.wikipedia.org/wiki/L-System
,
(2006).
Supplementary Information: Ryoichi Mizuno - Google+ 
