System Overview

L-systems (Lindenmayer systems) model biological growth through string rewriting. Starting with an axiom, rules recursively replace symbols to generate complex branching structures. Each iteration adds detail, creating fractal-like natural forms.

Phyllotaxis describes the spiral arrangement of leaves, seeds, or petals. The golden angle (137.5°) creates optimal packing, seen in sunflowers, pinecones, and many plants. This pattern emerges from simple mathematical rules.

Why Games Use This

• Procedural Plants: Generate infinite variety of trees, flowers, and vegetation
• Natural Aesthetics: Create organic, believable environments
• Memory Efficiency: Store rules, not full geometry
• Scalable Detail: Generate at different LODs by changing iterations
• Artistic Control: Tweak rules to create specific styles

Key Parameters

• Iterations: More iterations = more detail, but exponential growth
• Branch Angle: Controls spread of branches
• Branch Length: Size of each segment
• Phyllotaxis Angle: Spiral angle (137.5° is golden angle)
• Rules: Define how symbols transform

Failure Modes

• Too many iterations: Exponential string growth causes memory/performance issues
• Poor rule design: Rules that don't terminate create infinite loops
• Extreme angles: Very large angles create chaotic, unrealistic forms
• No termination: Missing base case in recursive rules
• Stack overflow: Deep nesting in bracket notation

Scaling Behavior

L-system string length grows exponentially with iterations. 5 iterations can produce strings with millions of characters. Limit iterations to 3-5 for real-time rendering. Use stochastic rules carefully as they prevent caching.

Phyllotaxis is O(n) for n points, making it very efficient. Can generate thousands of points in real-time.

Related Algorithms

• Stochastic L-systems: Random rule selection for variation
• Context-sensitive L-systems: Rules depend on neighbors
• Parametric L-systems: Rules with parameters for continuous variation
• Space Colonization: Growth based on attraction points
• Reaction-Diffusion: Chemical patterns for leaf venation

Free Tools & Libraries

• L-Py: Python L-system framework
• Structure Synth: 3D L-system generator
• Context Free: Grammar-based art tool

System-Thinking Prompts

• What happens at 10 iterations? How does string length explode?
• Where do L-systems break? Stack overflow, infinite rules?
• How could players exploit deterministic growth? Predictable patterns?
• Which parameter dominates? Iterations, angle, or length?
• What's the optimal phyllotaxis angle? Why 137.5°?
• How do stochastic rules affect determinism? Can we still cache?
• What's the minimum viable L-system? Simplest grammar?