L-system Generator
Generate complex fractals, space-filling curves, and organic plant patterns using Lindenmayer systems.
Last updated: May 29, 2026
Presets Library
Classic fractals & botanical rules
L-System Grammar
Define axiom & production rules
Styling & Backdrop
Colors, stroke, canvas background
L-system Generator — No Uploads Required
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.
Why This Tool Exists
What makes this useful — and why I built it this way.
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.
When You'd Use This
Real situations where this tool saves the day.
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.
Using L-system Generator
It's straightforward — here's how it works.
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'.
Questions People Ask
Honest answers about how this works.
What is an L-system?
Honestly? 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 exactly does the turtle interpret the symbols?
Honestly? 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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