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Riemannian L-systems: modelling growing forms in curved spaces
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
Summary
This study extends L-systems to model biological growth in curved, non-Euclidean spaces, integrating differential geometry for accurate simulations of plant development and branching systems.
Area of Science:
- Computational Biology
- Developmental Biology
- Mathematical Biology
Background:
- L-systems formalism effectively models biological growth in Euclidean spaces.
- Many biological forms grow in curved, non-Euclidean spaces, posing a challenge for existing models.
- Examples include plant venation, pollen tube growth, and tissue development.
Purpose of the Study:
- To extend the L-systems formalism to model biological growth in non-Euclidean spaces.
- To integrate differential geometry concepts into turtle geometry for curved space modeling.
- To demonstrate applications in plant development and abstract growth modeling.
Main Methods:
- Extension of L-systems formalism to non-Euclidean geometry.
- Integration of differential geometry into turtle geometry.
- Application to modeling mathematical and biological forms on curved surfaces.
Main Results:
- Successfully extended L-systems to model growth in curved spaces.
- Demonstrated applications in plant development, including vein networks and pollen tubes.
- Showcased extension to abstract Riemannian spaces for modeling growth on non-embedded curved substrates.
Conclusions:
- The extended L-systems provide a novel approach for modeling biological growth in complex, curved environments.
- This formalism enables more accurate simulations of plant development and other biological systems.
- The abstract extension offers potential for modeling growth in diverse, non-uniform substrates.
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