
Lindenmayer Systems
Zach Layton
A series of algorithmically generated images investigating issues of organic form.
http://www.zachlaytonindustries.com/Lsystems.htm
Classes
The Nature of Code
Keywords
L-Systems, Nature of Code
Description
I've always been interested in what John Cage referred to as making artwork as a process of "observing nature in her manner of operation". After studying in Daniel Shiffman's "Nature of Code" class, I found myself very interested in this process from a computational point of view. These Lindemeyer systems were originally created as a means of studying plant growth, though they have been commonly employed by artists for other purposes. I found it interesting to use these algorithms to create patterns that are highly abstracted from their more common contexts. There is an element of unpredictability to these forms, though the patterns are recursive, so there is also kind of logic to the forms as well. Finding a balance between logic and indeterminacy is what interests me about this project.
"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).
example:
If we define the following simple grammar:
variables : A B
constants : none
start : A
rules : (A → B), (B → AB)
then this L-system produces the following sequence of strings:
n=0 : A
n=1 : B
n=2 : AB
n=3 : BAB
n=4 : ABBAB
n=5 : BABABBAB
n=6 : ABBABBABABBAB
n=7 : BABABBABABBABBABABBAB
and if we count the length of each string, we obtain the famous Fibonacci sequence of numbers:
1 1 2 3 5 8 13 21 34 55 89 ... "
-wikipedia
"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).
example:
If we define the following simple grammar:
variables : A B
constants : none
start : A
rules : (A → B), (B → AB)
then this L-system produces the following sequence of strings:
n=0 : A
n=1 : B
n=2 : AB
n=3 : BAB
n=4 : ABBAB
n=5 : BABABBAB
n=6 : ABBABBABABBAB
n=7 : BABABBABABBABBABABBAB
and if we count the length of each string, we obtain the famous Fibonacci sequence of numbers:
1 1 2 3 5 8 13 21 34 55 89 ... "
-wikipedia
Personal Statement
I've always been interested in what John Cage referred to as making artwork as a process of "observing nature in her manner of operation". After studying in Daniel Shiffman's "Nature of Code" class, I found myself very interested in this process from a computational point of view. These Lindemeyer systems were originally created as a means of studying plant growth, though they have been commonly employed by artists for other purposes. I found it interesting to use these algorithms to create patterns that are highly abstracted from their more common contexts. There is an element of unpredictability to these forms, though the patterns are recursive, so there is also kind of logic to the forms as well. Finding a balance between logic and indeterminacy is what interests me about this project.
Background
"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).
example:
If we define the following simple grammar:
variables : A B
constants : none
start : A
rules : (A → B), (B → AB)
then this L-system produces the following sequence of strings:
n=0 : A
n=1 : B
n=2 : AB
n=3 : BAB
n=4 : ABBAB
n=5 : BABABBAB
n=6 : ABBABBABABBAB
n=7 : BABABBABABBABBABABBAB
and if we count the length of each string, we obtain the famous Fibonacci sequence of numbers:
1 1 2 3 5 8 13 21 34 55 89 ... "
-wikipedia
example:
If we define the following simple grammar:
variables : A B
constants : none
start : A
rules : (A → B), (B → AB)
then this L-system produces the following sequence of strings:
n=0 : A
n=1 : B
n=2 : AB
n=3 : BAB
n=4 : ABBAB
n=5 : BABABBAB
n=6 : ABBABBABABBAB
n=7 : BABABBABABBABBABABBAB
and if we count the length of each string, we obtain the famous Fibonacci sequence of numbers:
1 1 2 3 5 8 13 21 34 55 89 ... "
-wikipedia
Audience
anyone
User Scenario
Viewer looks at paper which is hung on wall.
Implementation
ink and paper.
Conclusion
algorithmic processes yield surprising and exciting results. I see this project as the beginning of a process that will hopefully continue for a long time.
Additional Documents
- lsystems - Main Image