L-system Generator
Generate complex fractals, space-filling curves, and organic plant patterns using Lindenmayer systems.
Presets Library
Classic fractals & botanical rules
L-System Grammar
Define axiom & production rules
Styling & Backdrop
Colors, stroke, canvas background
Professional L-system Generator for Everyone
An interactive Online L-system (Lindenmayer system) Generator that allows you to design and render beautiful mathematical fractals, recursive plants, trees, and space-filling curves. Choose from classical presets like the Koch Snowflake, Dragon Curve, Sierpinski Gasket, Hilbert Curve, and Fractal Plants, or input your own custom axiom and rewriting rules. The engine evaluates rules in real-time, calculates boundaries for automatic canvas scaling and centering, and draws the output using high-performance HTML5 canvas turtle graphics. Customize stroke width, joint caps, drawing speeds, and choose from stunning color modes including solid fills, linear gradients, and a multi-color rainbow cycle. Export your fractal art as scalable vector SVGs or high-resolution PNGs instantly. Processed completely in your browser for 100% privacy.
Key Benefits
Why choose our L-system Generator for your workflow?
Educational & Fun: Learn about formal grammars, recursion, self-similarity, and natural growth models.
Limitless Creativity: Combine different rules and iterations to generate unique geometric patterns.
Completely Secure: Runs locally in your browser, no server connections or tracking.
Common Use Cases
Real-world examples of how to use this tool.
Digital Art: Generate geometric, modern, or organic vector backgrounds and patterns.
Mathematical Education: Visualize fractals, recursive sequences, and turtle coordinates.
Botanical Modeling: Render realistic plant stalks, leaves, and dendritic structures.
How to use L-system Generator?
Follow these simple steps to get the best results.
Choose a pre-configured L-system preset, or customize the Axiom, Rules, Angle, and Iterations manually.
Adjust the drawing thickness, cap join styles, and choose your favorite color scheme.
Use the playback controls to play, pause, or draw instantly.
Drag on the canvas to pan and use the scroll wheel to zoom in on complex details.
Export your fractal creation by clicking 'Download PNG' or 'Download SVG'.
Frequently Asked Questions
Common questions about our L-system Generator tool.
What is an L-system?
An L-system (Lindenmayer system) is a parallel rewriting system consisting of an alphabet of symbols, an axiom (initial string), and a set of production rules that expand symbols into longer strings of symbols over successive iterations.
How does the turtle interpret the symbols?
The renderer reads the expanded string character-by-character: 'F' or 'G' moves the turtle forward drawing a line, '+' turns right by the specified angle, '-' turns left, '[' saves the current position and angle, and ']' restores the saved state.
Why are some iterations locked or slow?
Each iteration increases the length of the string exponentially. To prevent browser freezing, we limit maximum iterations and total string length to 150,000 characters.
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