Playful Python Project: Modeling and Animation by Mozgovoy Maxim

Author:Mozgovoy, Maxim
Language: eng
Format: epub
Publisher: CRC Press
Published: 2024-06-06T00:00:00+00:00

5.5 Lindenmayer Systems

In the previous projects we observed how simple entities, controlled by simple rules, could produce intricate movements. Now we will take the opposite direction by looking into complexly organized immovable objects. The specific topic of our interest is going to be Lindenmayer systems (or L-systems), created for studying the developmental process of plants and similar organisms [42].

Among the most conspicuous properties of a plant shape are symmetry and self-similarity. Symmetry is a common feature of many living things: the left half of a beech leaf is the mirror image of its right half; two “pizza slices” of a daisy flower look alike. Self-similarity is a more elusive concept, used to describe a structure consisting of elements that look similar to the whole. For example, a tree is “self-similar” because it consists of branches, organized in the same way as the tree itself. Likewise, a compound leaf (such as a fern leaf) consists of leaflets that look similar to the whole leaf.

The complexity of plant structure appears to be an emergent property, arising naturally in the course of the normal plant growth. In other words, we again deal with a complex outcome, produced by a relatively simple process.

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 3Fun fact: remember that these boids are actually flying turtles in our case. While the original motivation for creating L-systems was to study and model the actual laws behind the process of plant growth, our goal is going to be more modest. In case of boids, we were interested in making the onscreen objects move somewhat like birds, and now we will try to generate patterns that look somewhat like plants.

In a nutshell, L-systems are based on three foundational ideas. The first idea is to represent plant structure with a string of characters. For example, suppose that a certain type of a plant is made of three kinds of elements: a trunk element I, a left leaf L, and a right leaf R. A little specimen of this plant, consisting of a single trunk element and two leaves, can be described with a string LRI (see Figure 5.5). Note that any particular image is just an illustration of one of many possible looks of the LRI plant. The textual description does not really dictate any particular appearance, it is only responsible for the internal structure of the entity we describe.

Figure 5.5: LRI plant.

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