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Riemannian L-systems: modelado de formas en crecimiento en espacios curvos
Christophe Godin1, Frédéric Boudon2,3
1Laboratoire Reproduction et Développement des Plantes, Univ. Lyon, ENS de Lyon, UCB Lyon1, CNRS, INRAE, Inria, Lyon, France.
Quantitative plant biology
|December 25, 2025
Resumen
Este estudio extiende los L-systems para modelar el crecimiento biológico en espacios curvos y no euclidianos, integrando la geometría diferencial para simulaciones precisas del desarrollo de plantas y sistemas de ramificación.
Área de la Ciencia:
- Biología Computacional
- Biología del Desarrollo
- Biología Matemática
Sus antecedentes:
- El formalismo de los L-systems modela eficazmente el crecimiento biológico en espacios euclidianos.
- Muchas formas biológicas crecen en espacios curvos y no euclidianos, lo que supone un desafío para los modelos existentes.
- Los ejemplos incluyen la venación de las plantas, el crecimiento del tubo polínico y el desarrollo de tejidos.
Objetivo del estudio:
- Extender el formalismo de los L-systems para modelar el crecimiento biológico en espacios no euclidianos.
- Integrar conceptos de geometría diferencial en la geometría de tortuga para modelar espacios curvos.
- Demostrar aplicaciones en el desarrollo de plantas y el modelado de crecimiento abstracto.
Principales métodos:
- Extensión del formalismo de los L-systems a la geometría no euclidiana.
- Integración de la geometría diferencial en la geometría de tortuga.
- Aplicación al modelado de formas matemáticas y biológicas en superficies curvas.
Principales resultados:
- Extensión exitosa de los L-systems para modelar el crecimiento en espacios curvos.
- Demostración de aplicaciones en el desarrollo de plantas, incluyendo redes de venas y tubos polínicos.
- Exhibición de la extensión a espacios riemannianos abstractos para modelar el crecimiento en sustratos curvos no embebidos.
Conclusiones:
- Los L-systems extendidos proporcionan un enfoque novedoso para modelar el crecimiento biológico en entornos curvos complejos.
- Este formalismo permite simulaciones más precisas del desarrollo de plantas y otros sistemas biológicos.
- La extensión abstracta ofrece potencial para modelar el crecimiento en sustratos diversos y no uniformes.
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