Animated Fractal Trees

This page lets you create complex structures based upon the recursive repetition of simple geometric rules. These structures are named L-Systems after Aristid Lindenmayer, a Hungarian theoretical biologist and botanist who developed and introduced them in 1968.

L-systems often resemble plants or trees. Use this page to explore L-systems and create your own unique animated structures.

Examples 1-3 are animated structures. Examples 4-5 are single frame non-animated structures.

Here are some example L-systems that you can view and modify.

1. A Tree  

2. Spiral Plant  

3. Koch Snowflake  

4. Sierpinski Triangle  

5. Fractal Tiles  


2. Spiral Plant 

Settings


Title (optional)
Axiom
Rules
Iterations
Line Width pixels (0 for auto)
Animation Frames
Turn Angle (Start) degrees
Turn Angle (End) degrees
Step Size (Start)
Step Size (End)
Display Size pixels

Instructions

The basic rules are:

F Draw forward
Turn clockwise
+ Turn anti-clockwise
[ Save the current values for position and angle
] Restore the previously saved position and angle

There are two additional rules to modify the draw colour:

> Increment colour index
< Decrement colour index

To create a structure define an axiom and a set of rules that employ the commands above.

Other available options are:

Number of iterations
Line width
Number of animation frames
Turn angle
Step size
Display size

Click the 'Generate' button to create and display the fractal tree animation.

The bookmark link contains a URL to view and edit the current fractal tree.

Useful Links

L-System Wikipedia Article
The Nature of Code by Daniel Shiffman, Chapter 8. Fractals
The Algorithmic Beauty of Plants

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