L-Systems Explorer

Lindenmayer Systems: Fractal Growth Through String Rewriting

Preset Gallery

Rule Designer

Animation

About L-Systems

L-Systems (Lindenmayer Systems) were introduced by biologist Aristid Lindenmayer in 1968 to model the growth patterns of plants. These parallel rewriting systems use simple rules to generate complex, self-similar structures that closely resemble natural forms.

String Rewriting: An axiom is recursively transformed using production rules
Turtle Graphics: The resulting string is interpreted as drawing commands
Applications: Plant modeling, fractals, procedural generation in CGI and games
Self-Similarity: Each iteration reveals increasing detail at finer scales

Create Custom L-Systems

Design your own fractal structures by defining an axiom (starting string) and production rules. The turtle graphics interpreter recognizes these commands:

F: Draw forward by segment length
+ / -: Turn right/left by angle
[ / ]: Push/pop turtle state (position and angle)
X, Y: Non-drawing symbols (used for structure only)

Axiom:

Rules:

Angle: 22.5°

Iterations: 4

Segment Length: 8

Line Width: 1.5

Current Iteration

Total Segments

String Length

Watch Growth Over Time

Observe how L-Systems evolve iteration by iteration. Each generation applies the production rules to the current string, revealing the emergent fractal structure step by step.

Select Preset:

Speed: 500ms

Current Iteration

Segments Drawn

String Length