L-Systems

Hello! This is the code for my Computerphile video, https://youtu.be/puwhf-404Xc.

It runs user-defined L-systems using Python's turtle module, and also can simulate graphical effects such as random angles and segment lengths, and tropism (where the plant points towards the "sun").

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Also, huge thanks to Alex for checking over the code, making sure it runs on his macOS ("it works on my machine" and all that), writing the "installing Tkinter" instructions in this document, and writing the code for selecting L-systems upon running the code!

If you have any trouble at all setting this up, feel free to email me, contact me via the details on my website, or simply raise an issue on this repository and I'll help you out.

Quickly getting started

If you just want to see pretty pictures, follow these steps:

1. Install Python if you haven't already.
2. Download this repository (either via cloning it or just downloading it directly as a ZIP).
3. Install the Tkinter graphics library if if you don't have it.
   • Windows: Should be installed with python. If not, run 'pip install tk' in comand prompt.
   • MacOS: Easiest to do by running 'brew install python-tk' if you have homebrew.
   • Linux: Package name differs between 'tk', 'python3-tkinter', 'python-tk' among others, depending on your distribution.
4. Run the Python script lsystem.py.
   • Through the command line, this is python3 lsystem.py.
   • You might be able to just double click the file - I'm not sure.
   • You'll be asked for which system to see, type the name of the given system and press enter.
5. That's it! I'd recommend full-screening the window, then press ENTER a few times to advance the simulation.
   • You can go into "slow mode" by pressing DOWN (and back to fast by pressing UP) if you want to show the image as it is being drawn.

Making your own L-system

If you want to make your own L-system, follow these steps:

1. Download the Python script as described previously.
2. Open lsystem.py in your editor of choice and scroll down to line 92. There are lots of L-systems defined here, the custom default of which is currently a copy of "cow parsley", between lines 171 and 198.
3. Edit the rules to your liking!
   • The rules are defined as a Python dictionary in rules.
   • The turning angle is defined as a float in angle.
   • The initial/seed sequence is defined in axiom.
   • Any upper-case letter is interpreted as a stem segment.
   • [ and ] are interpreted as described in the video (i.e. branching).
   • - and + are interpreted as rotation left and right by angle.
   • Any other symbols are skipped while drawing the picture, so they can be used for "structural elements" (see the Hilbert curve).

Using the funky rendering features

I've implemented a few things here which can make your drawings look more realistic and lifelike. Once you've defined an L-system, you can play with these variables:

• tropism_angle: the angle to turn towards as if pointing at the sun. Measured counter-clockwise in degrees from due east.
• tropism_amount: the amount of tropism to apply at each turn. This should usually be very small, like 0.05 or such. Setting this to 0 turns off tropism, and is the default value.
• angle_random_variation, length_random_variation: the amount by which the rotation angle and the segment length should vary. Given as the standard deviation of a normal distribution about the means angle and line_length respectively.
• bud_symbols: a string containing symbols which should be interpreted as flower buds (i.e. which should render with a white circle at the end).
• default_pen_size: the thickness of the stem lines (default 2).
• line_length: the mean segment length (default 10).
• start_pos: the position on the screen to start at, as a tuple. The screen opens as an 800x800 window, and (0, 0) is the center (default (0, -380)).
• sub_chance: the probability that each rule substitution will take place. Default 1.0. Reducing this can lead to some cool effects.