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Tobias
A 30+ year old Msc. Graduate in Computing Science currently working in the financial technology sector.
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Wednesday, August 4, 2010

L-system


Here is a personal favorite of mine. L-system is short for Lindenmayer system, as in Aristid Lindenmayer the hungarian biologist who introduced this technique in 1968. L-system is related towards formal grammar mostly known for describing the growth process of plants. The growth algorithm itself is recursive and often pretty simple, but the result is far more complex. The very nature of the process makes the L-system categorized to self-similarity, meaning that even a small part of the plant is similar to it's whole structure.

The plant has its point of origin which never changes, however how the plant grow is formalized recursivly through a number of iterations where every iteration has one or several sets of rules which discribes the growthprocess. This is an important difference between L-system and formal grammar where there only is one rule.

There are many offsprings of Lindenmayers original L-system, but we for now only focus on one - The Fractal plant. I'm going to use the wiki example because I think it's self-explanatory.

variables
: X F
constants
: + −
start
: X
rules
: (X → F-[[X]+X]+F[+FX]-X), (F → FF)
angle
: 25°
Here, F means "draw forward", - means "turn left 25°", and + means "turn right 25°". X does not correspond to any drawing action and is used to control the evolution of the curve. [ corresponds to saving the current values for position and angle, which are restored when the corresponding ] is executed.


Pretty life-like wouldn't you say? This is just an example of how L-system may be used, as I said earlier there are many variations. The emergent part is the simplicity, two rules howto draw lines produces this. If you look closely you can see the self-similarity in every branch. So what can we do next, well the video below is one thing.



I will return to L-system later to do some deeper analysis. For now ... as allways ... I leave it to you to find out more for yourself.

- Tobias

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