# L-system generator

## World's simplest math tool

Free online Lindenmayer system generator. Just enter the axiom and rewrite rules and you'll automatically get a visualization of the grammar. There are no ads, popups or nonsense, just an awesome L-system viewer. Press a button — visualize a Lindenmayer system. Created by mathematicians for mathematicians.

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L-system generator tool
What is a l-system generator?

This tool draws and visualizes L-system rules. The L-system is also known as the Lindenmayer system. It consists of an alphabet of symbols, a starting axiom and a set of rules that define how symbols get rewritten. With this tool you can specify which symbols to visualize, which symbols to skip, and how many iterations of rewriting to perform. Because of the recursive nature of the rewrite system it often produces self-similar fractals. Symbols plus (+) and minus (-) have a special meaning and they change the curve direction by the specified angle. You can set the dimensions for your L-system and choose the drawing start direction. To make it more visually appealing, you can also set the color for the background and for the curve line, set the line thickness and padding. To share your creation you can click the link icon and get a URL to the L-system you created. Mathabulous!

L-system generator examples
Click to use

Draw a Gosper Curve

This example uses L-system rules to generate a fractal Gosper curve. It uses four iterations and angle of 60 degrees. Background is set to green and line width to 4px.

**Required options**

Draw these symbols.

Skip these symbols.

Starting axiom.

Rewrite rule 1.

Rewrite rule 2.

Curve width.

Curve height.

How many iterations to perform?

Angle of rotation.

Thickness of a curve.

Padding around the image.

Background color.

Curve color.

Draw a Red Dragon Curve

This example generates a 10th order dragon curve using simple L-system rewrite rules. We set background to red as dragons love to spit fire. The L-system dimensions are set to 500x400px.

**Required options**

Draw these symbols.

Skip these symbols.

Starting axiom.

Rewrite rule 1.

Rewrite rule 2.

Curve width.

Curve height.

How many iterations to perform?

Angle of rotation.

Thickness of a curve.

Padding around the image.

Background color.

Curve color.

Draw an Icy Fractal

In this example a curve similar to freezing ice pattern is created by a single Lindenmayer system rule. We used cold colors to make it look like a real frost.

**Required options**

Draw these symbols.

Skip these symbols.

Starting axiom.

Rewrite rule 1.

Curve width.

Curve height.

How many iterations to perform?

Angle of rotation.

Thickness of a curve.

Padding around the image.

Background color.

Curve color.

Draw a Fractal Tree

This example visualizes L-system rules that look like a tree. This curve has an angle of 36 degrees and is 3 iterations deep. We used special symbols [ and ] in the first rule that mean save the current curve position to stack, and restore the position from stack.

**Required options**

Draw these symbols.

Skip these symbols.

Starting axiom.

Rewrite rule 1.

Curve width.

Curve height.

How many iterations to perform?

Angle of rotation.

Thickness of a curve.

Padding around the image.

Background color.

Curve color.

Draw a William McWorter's Pentadendrite

This example generates a McWorter's Pentigree curve using just one L-system rewrite rule with a rotation angle of 72 degrees. It also sets iterations to 4, padding to 5px and width of curve's line to 2px.

**Required options**

Draw these symbols.

Skip these symbols.

Starting axiom.

Rewrite rule 1.

Curve width.

Curve height.

How many iterations to perform?

Angle of rotation.

Thickness of a curve.

Padding around the image.

Background color.

Curve color.

Draw a Round Star

This example displays a non-standard L-system with an angle of 77 degrees. This curve consists of straight lines, which simultaneously form both a star and a circle.

**Required options**

Draw these symbols.

Skip these symbols.

Starting axiom.

Rewrite rule 1.

Curve width.

Curve height.

How many iterations to perform?

Angle of rotation.

Thickness of a curve.

Padding around the image.

Background color.

Curve color.

Draw a Island Curve

This example generates a L-system, which consists of many small rectangles that look like islands. There are two special restrictions here. The F symbol is used for drawing but the b symbol is skipped (if you remember that an L-system is just a turtle that walks around a canvas leaving a trace for every alphabet symbol, then the b symbol makes turtle move ahead without drawing a line segment).

**Required options**

Draw these symbols.

Skip these symbols.

Starting axiom.

Rewrite rule 1.

Rewrite rule 2.

Curve width.

Curve height.

How many iterations to perform?

Angle of rotation.

Thickness of a curve.

Padding around the image.

Background color.

Curve color.

Draw a Penrose Tiling

This example uses an L-system to generate a Penrose tiling. For this curve we use all 5 rules and use four characters for drawing. We also set the color of the background to black and yellow color for the line. Pretty!

**Required options**

Draw these symbols.

Skip these symbols.

Starting axiom.

Rewrite rule 1.

Rewrite rule 2.

Rewrite rule 3.

Rewrite rule 4.

Rewrite rule 5.

Curve width.

Curve height.

How many iterations to perform?

Angle of rotation.

Thickness of a curve.

Padding around the image.

Background color.

Curve color.

Draw a Koch curve

This example generates a variation of Koch star known as Cesero fractal with an angle of 80 degrees. It has a width of 600px and a height of 400px, it uses 6 iterations and the starting direction is set to left.

**Required options**

Draw these symbols.

Skip these symbols.

Starting axiom.

Rewrite rule 1.

Curve width.

Curve height.

How many iterations to perform?

Angle of rotation.

Thickness of a curve.

Padding around the image.

Background color.

Curve color.

Pro tips
Master online math tools

You can pass options to this tool using their codes as query arguments and it will automatically compute output. To get the code of an option, just hover over its icon. Here's how to type it in your browser's address bar. Click to try!

https://onlinemathtools.com/l-system-generator?&angle=60&draw=AB&skip=&axiom=A&rule-1=A%3DA-B--B%2BA%2B%2BAA%2BB-&rule-2=B%3D%2BA-BB--B-A%2B%2BA%2BB&width=400&height=400&iterations=4&direction=right&line-width=4&padding=5&background-color=%23014d0b&line-segment-color=%23d5ffc1

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