Overview
An L-System starts with an axiom string and applies production rules over several generations, often drawing the result with turtle graphics.
ExtendedSource checked
L-System
Generates structures by repeatedly rewriting symbols with grammar rules.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Procedural Generation
- Difficulty
- Beginner
- Family
- Grammar Generation
- Tier
- Extended
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 0
- Relationships
- 5
- Code example
- Not ready
- Visualization
- Ready
- Aliases
- Lindenmayer System
Core Concepts
generated structuresymbol rewritingmulti-scale detailgrammar generationseeded variationrule expansionspatial structure
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(n)
Average
O(n g)
Worst
O(n g)
Space
O(n)
When to Use
- Use L-System when you need to rewrite symbols in parallel.
- Use it for plant generation with inputs like axiom.
- Use it when repeatable content can be produced from compact rules, parameters, and seeds.
- Use it when the Grammar Generation tradeoff is acceptable for the problem size.
When Not to Use
- Avoid it when authored control matters more than variation or replayability.
- Avoid it when the required output is not generated symbol string or geometry.
What It Does
- Rewrites symbols in parallel
- Interprets the final string as structure or drawing commands
Use Cases
- Plant generation
- Fractal curves
- Rule-based patterns
Inputs
- Axiom
- Production rules
- Iteration count
Outputs
- Generated symbol string or geometry
Pseudocode
- 1.Start with the axiom string
- 2.For each generation, replace every symbol using production rules
- 3.Keep symbols without rules unchanged
- 4.After the final generation, interpret symbols as drawing commands
- 5.Return the generated structure
Canonical Example
- Input
- axiom = 'F', rule = F -> F+F, iterations = 2
- Output
- string = 'F+F+F+F'
- Explanation
- L-System: The L-System rewrites each F in parallel for each generation.
Implementation Notes
- Keep the input contract explicit: Axiom; Production rules; Iteration count.
- Use this step as the implementation spine: Start with the axiom string.
- Then preserve the next state change: For each generation, replace every symbol using production rules.
- Expose seed and parameters so results can be reproduced and tuned.
Common Pitfalls
- Small rule changes can produce very different structures.
- Letting random choices create disconnected, invalid, or impossible-to-use output.
- Returning generated symbol string or geometry without handling empty, invalid, or boundary inputs.
Interactive Mechanism Walkthrough
Spatial Primitive & Sweep-Line CanvasShow symbols expanding into branching plant-like geometry.
Step 1 of 5: Start with the axiom string
grammar-growthNotes
L-System operates in O(n g) time and O(n) space within the Grammar Generation family. Often compared with Recursive Descent Parsing and Domain Warping.
Sources (1)
What each reference supports for this entry.
The Algorithmic Beauty of Plants
BookReference for L-system rewriting rules and plant-like procedural structures.
Open sourceExplore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Variant ofGrammar-Based Generation
Procedural Generation · Core
L-systems use rewriting rules for recursive structures.
Compare with thisRelationships
View full relationship pageVariant ofGrammar-Based Generation
L-systems use rewriting rules for recursive structures.
Conceptual neighborSpace Colonization Algorithm
Both are common procedural plant or branching structure methods.
Related Algorithms
Tags
Procedural GenerationGrammar GenerationFractal