CLASS NOTES
Cellular Automata have
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a lexicon of states
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a set of transformation rules
L-System models (L is short for Lindenmeyer):
L-Systems have
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a lexicon of parts
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a set of transformation rules
Micro-Botany-Lesson
Plants are different from animals, with grow by increasing in size, in that they are made of parts (called metamers) and they grow by increasing the number of parts. Plant growth is decentralized. L-systems are useful for modeling other things, like ant colony tunnels, that exhibit decentralized growth. Each metamer has only two places on a metamer where cells actually divide: the apical meristem and the axillary meristem 
.
A simple l-system will have a 1-word lexicon. The rules will tell the program when and where (axial or axillary position) to add a metamer.
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similar to a CA because every metamer is asked whether another metamer should be added to it
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different from a CA because the number of metamers grows. The number of cells in a CA stays the same.
Example of and L-system model of a tree ( See LsystemTreeCode ). Note: python does trig in radians.
The program described in this code uses recursion. In order to execute the command "do-metamer" on one metamer, it has to "do-metamer" on the next one in line. Once that's done, it can finish executing the command for the first one.
We looked at the trees draw by the program. Some were very small, others were big. Why? -- The trees grow exponentially. Early decisions constrain later possibilities. So, if, early in the execution of the program, the tree decides not to add a metamer, the potential for other metamers to be added in the remaining time steps decreases.
What doesn't this model include?
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environmental factors : gravity, herbivores, nutrients
What's good about this model?
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high level of generality
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describes how local dynamics influence global behavior
L-systems posters at botany poster sessions: trees that look like they came out of a PIXAR movie. botanists say: "those things make pretty pictures, but they're not real science."
note: many real trees species seems to have collision avoidance mechanisms
note: in netlogo, #of turtles = #of meristems.
to do: look at trees around campus. what kind of "thinning rule" would you write to model the relative thickness of branches and trunk as a function of height or distance along the network?
Back to the posters: What does it mean if you can come up with an L-system that makes a picture that looks exactly like an oak? Have you explained the tree?
L-systems sacrifice realism and predictiveness for generality. They provide a way to assess the relative importance of different variables.
Every explanation is a simplification. Would the best model of something be an exact replica? -- No, because it would be a re-creation, not an explanation.
In what way(s), and how well, does your model need to fit the thing you're modeling?
Your predictions need to be ones that everybody can agree on whether or not they've been satisfied.
But, be careful, because too-specific predictions can be self-fulfilling.
