Fun with Python

Fun with Python is a series of python scripts where I code things I find funny!

Fractal Trees

This script uses the turtle module which is a library for easily drawing on screen.
It works by having a pointer, the turtle, which you can move around the screen. You can lift and lower the pen to enable the "draw mode" and move the turtle to trace a line.
The library also enables you to change the pen stroke width and the both the pen color and the background color.

How the script works

To draw the fractal tree the program starts from a specific point and draw a line using polar coordinates (length and heading).
It saves the current position of the turtle and stores it in a "node" structure (a tuple of the type (position, heading)).
It then calls the draw_fractal_tree function which takes in a list of nodes.
For each node the turtle will draw the left and right branches, changing its heading every time by a given amount (left_angle, right_angle).
Each time a new branch is drawn, the function also pushes the current node (turtle position and heading) into a list (next_starting_positions).
Once every node has its pair of left and right branches drawn, the function calls itself (recursion) using as function parameter the next_starting_positions list.
Thanks to a counter, the function will stop recursively calling itself once the number of generations has reached the desired amount (NUM_GENERATIONS).

This results in having a pair of branches popping out from every node, which in turn is part of a pair originated from another branch ending (node) of the previous generation.

The tree is thus built and can be rendered on screen.

Running the script

Once you've downloaded fractal_trees.py you can run the script with the command: python fractal_trees.py.
In this case, the program will generate the fractal tree using the parameters specified in code.

You can also use some options:

• -r to randomize the tree parameters
• -l <file_name> to load a the fractal tree parameters at ./trees/<file_name>.json
• -s <file_name> to save the current fractal tree parameters to ./trees/<file_name>.json

The fractal tree parameters

The fractal tree is defined by various parameters:

• left_angle: the bending angle for left branches
• right_angle: the bending angle for right branches
• length_multiplier: the branch length ratio between the current generation and the previous one
• starting_length: the length of the first branch
• starting_angle: the bending angle for the first branch
• starting_width: the width of the first branch (makes a gradient with ending_width)
• ending_width: the width of the last branches (makes a gradient with starting_width)
• generations_number: the number of branch layers (a generation can be defined as the set of braches with the same length)
• background_color: the background color
• starting_tree_color: the color of the first branch (makes a gradient with ending_tree_color)
• ending_tree_color: the color of the last branches (makes a gradient with starting_tree_color)

Remember: all angles are given in degrees, 0 is north and angles are positive when turning counter-clockwise, negative when turning clockwise.

An example fractal tree

{
    "left_angle": 30,
    "right_angle": 50,
    "length_multiplier": 0.6,
    "starting_length": 250,
    "starting_angle": 0,
    "starting_width": 15,
    "ending_width": 2,
    "generations_number": 8,
    "background_color": [0, 0, 0],
    "starting_tree_color": [0.6, 0.4, 0.2],
    "ending_tree_color": [0.2, 0.8, 0.2]
}