The Parallels between L-System & Hierarchical Levels of Plant Development through Recursive Growth

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(Prusinkiewiczy et al., 1996)

An L-System model is a mathematical system founded by the Hungarian botanist, Aristid Lindenmayer, used to model cellular development through an algorithm containing repeating strings of exponential growth (Pike 2007).

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Figure 2 Shows a simplified visual of the L-System structure (Prusinkiewiczy et al., 1996).

There are a few elements needed to set up an L-System (Figure 2). An alphabet (variables A & O), an axiom (A), and a set of rules to define the pattern of transformations (A→AO & O→A). An axiom is the element placed at the beginning of the system. This system uses recursive logic to generate a sentence over and over again using “string replacement”. The program will eventually terminate according to the parameters determined within the initial equation (n! = n x n-1). This usually occurs when “n” is less than one. Once complete, the system will visually represent a fractal organization of elements.  This structure in itself can be seen in multiple levels of hierarchy within plant biology (Figure 1). The system of algorithms persists from a cellular level of an individual plant all the way up to the rules defining the organization of many plants within a forest.

Figure 1 Multiple developmental stages of hierarchy in shoot and foliage L-System growth (Prusinkiewiczy et al., 1996).

For example, a tree demonstrates recursive behavior of branch growth. What this means is that the tree trunk is equivalent to itself in terms of the branching pattern. So, if we were to define rules for the branches of the tree, we could say the branch is equivalent to a line. The first point on the line is the beginning of the tree and the second point is the point of dissection of new branches. If every branch is said to have two branches, the two branches from the original branch would also branch into two branches, which would branch into two branches, and so on.

This algorithm becomes super nifty when incorporating the same logic within a computer program software to output graphics resembling organic growth. This enables effortless simulations of growth within the development of a plant at multiple scales.

Parameters of this program can also be manipulated to fit an array of scenarios such as: simulations of fractal formations within a leaf, developmental sequence of the stylized compound leaf, modeling mesotonic and acrotonic structures( Figure 3), shedding of branches, patterns of plant response and recovery throughout the attack of a predator, and predictions of growth response to certain modifications such as pruning (Prusinkiewiczy et al. 1996).

Figure 3 (Prusinkiewiczy et al., 1996).

In summary, the L-System can be applied to most forms of morphogenesis within and across vast networks of plant biology. The ability to capture this process of development is extremely useful when paired with programming, because it enables the generation of visual simulations of an organism’s form in correlation to the driving mechanism behind it. Once a visual representation is generated, one can specify how certain properties are affected by external events and accurately predict the impact of certain events. This is exciting news because the system requires minimal data and effort and can be replicated easily using a computer and some computer programming skills.

Figure 4 (Prusinkiewiczy et al., 1996).

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Citations:

Leitnerand, D., & Schnepf, A. (2009). ROOT GROWTH SIMULATION USING L-SYSTEMS.

Birchler, B., & Krug, P. (1996). A plant diagnosis system takes its first steps. World Pumps, 1996(356), 54–56. doi: 10.1016/s0262-1762(99)80766-4

Pike, A. (2007). Modeling Plants with Lindenmayer Systems. SFU Computing Science, CMPT 461. doi: 10.3897/bdj.2.e1108.figure2f

Prusinkiewiczy, P., Hammel, M., Hanan, J., & Mech, R. (1996). L-SYSTEMS: FROM THE THEORY TO VISUAL MODELS OF PLANTS. 2nd CSIRO Symposium on Computational Challenges in Life Sciences, 1–32. Retrieved from http://algorithmicbotany.org/papers/l-sys.csiro96.pdf

Yurtoğlu, N. (2018). http://www.historystudies.net/dergi//birinci-dunya-savasinda-bir-asayis-sorunu-sebinkarahisar-ermeni-isyani20181092a4a8f.pdf. History Studies International Journal of History, 10(7), 241–264. doi: 10.9737/hist.2018.658

Yurtoğlu, N. (2018). http://www.historystudies.net/dergi//birinci-dunya-savasinda-bir-asayis-sorunu-sebinkarahisar-ermeni-isyani20181092a4a8f.pdf. History Studies International Journal of History, 10(7), 241–264. doi: 10.9737/hist.2018.658

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