In 1968, Hungarian botanist Aristid Lindenmayer developed a grammar-based system to model the growth patterns of plants.
This technique can be used to generate the recursive fractal patterns.
An L-system has three main components:
- Alphabet: An L-system’s alphabet comprises the valid characters that can be included.
- Axiom: The axiom is a sentence (created with characters from the alphabet) that describes the initial state of the system.
- Rules: The production rules of an L-system describe ways of transforming the sentence. Consta de un predecesor y sucesor.
El proceso de aplicar las reglas sucesivamente se denomina Generación.
- La Generación-0 es el mismo axioma.
- Las subsiguientes Generaciones resultan de aplicar las reglas a la generación anterior.
Por ejemplo, consideremos:
Alphabet A, B
Axiom A
Rules A → AB
B → A
Generation Sentence
G-0 A
G-1 AB
G-2 ABA
G-3 ABAAB
...
How Lindenmayer was able to translate strings of characters into the organic structures of plants.
Consideremos el alfabeto: F, G, +, –, [ and ]
donde,
FDraw a line and move forward.GMove forward (without drawing a line).+Turn right.–Turn left.[Save current state.]Restore current state.
Nota: El ángulo de giro es arbitrario.
This type of drawing framework is often referred to as turtle graphics.
Ejemplo:
Alphabet F, G, +, –, [, ]
Axiom F
Rules F → FF+[+F–F–F]–[–F+F+F]
Aplicando 4 generaciones y angulo 22.5º, resulta:
Mas figuras:
Reemplazar los datos en el código fuente para reproducir las figuras:
$n$ indica el número de generaciones a iterar.$\delta$ indica el angulo en grados.
- The Nature of Code - Fractals: https://natureofcode.com/fractals/#l-systems
- The Algorithmic Beauty of Plants https://algorithmicbotany.org/papers/#abop
- Author: Carlos Ramos
- Linkedin: https://www.linkedin.com/in/carlosramos05/
- GitHub: https://github.com/carlosfelipe14