Animated Fractal Trees
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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.
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Here are some example L-systems that you can view and modify.
1. A Tree
Settings
Instructions
The basic rules are:
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F | Draw forward
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− | Turn clockwise
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+ | Turn anti-clockwise
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[ | Save the current values for position and angle
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] | Restore the previously saved position and angle
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There are two additional rules to modify the draw colour:
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> | Increment colour index
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< | Decrement colour index
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To create a structure define an axiom and a set of rules that employ the commands above.
Other available options are:
Number of iterations
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Line width
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Number of animation frames
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Turn angle
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Step size
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Display size
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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