# What have the L-systems (Lindenmayer systems) been actually used for in biology?

From Wikipedia:

An L-system or Lindenmayer system is a parallel rewriting system and a type of formal grammar.

L-systems were introduced and developed in 1968 by Aristid Lindenmayer, a Hungarian theoretical biologist and botanist at the University of Utrecht. Lindenmayer used L-systems to describe the behaviour of plant cells and to model the growth processes of plant development.

I tried to find biological research that has actually used this system but I could not find any. Perhaps this is because I do not know biology that well.

Are these models important? Still taught?

They do produce pretty pictures (again from Wikipedia)

• The Wikipedia article points (in the references at the end) at least to a potential impact in developmental biology with this book (which I haven't read): amazon.com/… Jun 29, 2015 at 15:31
• BTW awesome images. Jun 29, 2015 at 15:32
• The main point is not that biologists do use l-systems in their research (although those interested in artificial life do), but that plant growth is (in mathematical sense) a l-system. Jun 29, 2015 at 19:29
• I've been considering using them to produce realistic branching in neural simulations, but I haven't actually implemented anything yet. Jun 29, 2015 at 23:43
• Great photos... here's a paper from Researchgate that may help you. I suggest reading the abstract + intro thoroughly and skimming over the paper. researchgate.net/publication/… Aug 5, 2016 at 17:32

Are these models important? Still taught?

Yes!! These models are extremely important, however, the application of L-systems most definitely isn't confined to just the scope of Biology. I myself first came across L-systems when taking Calculus in university, and then later in several Computer Science courses (I study Bioinformatics).

What's (probably) most significant to mention about L-systems is that they produce fractals, which is acheived by defining a substitution system and utilizing recursion.

Fractal mathematics can be used to describe extremely complex phenomena, starting with just a few simple rules and initial conditions (which is why it's so powerful/attractive to study). Also, fractals have the nickname of, "God's Thumbprint", or, "The Fingerprint of God", just from where they're found so prevalently in nature. To name a few, fractals can "easily" model:

• Coastlines
• Blood vessels
• Brain structure (neuronal connectivity)
• Plant foliage
• Lightning bolts
• Diamonds
• Snowflakes

I tried to find biological research that has actually used this system but I could not find any.

As you can see, some of these examples are biologically related, however, the use of L-Systems have been broadened to many other fields of science, such as mathematics (coding theory) and theoretical computer science.

Unfortunately, very rarely do biologists have the mathematical or algorithmic backgrounds to work with L-systems, since L-systems are more related to mathematics, algorithms and logic, than they are with (practiced) biology.