Drawing Recursive Trees with Python’s Turtle Library

Python’s turtle graphics library is a great tool for teaching programming concepts visually. One such concept that can be beautifully demonstrated using the turtle module is recursion, specifically when it comes to drawing fractal trees. In this blog post, we will explore how to use the turtle module to draw recursive trees.

Understanding Recursion

Recursion is a programming technique where a function calls itself to solve a problem. In the context of drawing trees, recursion allows us to break down the problem of drawing a complex tree into drawing smaller, simpler trees. Each subtree is a scaled-down version of the original tree, and the process continues until a base case is reached.

Implementing Recursive Trees with Turtle

To draw a recursive tree using the turtle module, we need to define a function that represents a single branch of the tree. This function will draw a line representing the branch, and then recursively call itself to draw the sub-branches.

Here’s an example implementation:

pythonimport turtle

# Set up the turtle
screen = turtle.Screen()
screen.bgcolor("skyblue")
tree = turtle.Turtle()
tree.speed(0)  # Fastest speed
tree.left(90)  # Start with the turtle facing upwards
tree.up()
tree.backward(150)  # Move the turtle to the starting position
tree.down()
tree.color("sienna")

# Function to draw a recursive tree
def draw_tree(branch_len, t):
    if branch_len < 3:
        return
    else:
        angle = 20
        t.forward(branch_len)
        t.right(angle)
        draw_tree(branch_len - 15, t)
        t.left(angle * 2)
        draw_tree(branch_len - 15, t)
        t.right(angle)
        t.up()
        t.backward(branch_len)
        t.down()

# Call the function to draw the tree
draw_tree(75, tree)

# Keep the window open
turtle.done()

In this code, we first set up the turtle with a blue background and adjust its initial position and orientation. The draw_tree function takes two parameters: the length of the branch and the turtle object. It checks if the branch length is less than a threshold (in this case, 3), and if so, it returns without drawing anything. Otherwise, it draws the branch by moving the turtle forward, turns the turtle to the right by a certain angle, and then recursively calls itself to draw the sub-branches. The process continues until the base case is reached.
Exploring the Code
There are a few key points to note in the code:

Recursion Base Case: The draw_tree function has a base case that checks if the branch length is less than 3. This ensures that the recursion stops at some point and prevents infinite recursion.
Drawing the Branch: The function uses the turtle’s forward method to draw the branch. The length of the branch is reduced by 15 for each recursive call to create the fractal effect.
Turning the Turtle: The turtle is turned to the right by a certain angle (angle) before drawing each sub-branch. This angle controls the branching pattern of the tree.
Backtracking: After drawing a sub-branch, the turtle is moved back to its original position using the backward method. This allows it to continue drawing the remaining sub-branches.

Conclusion
Drawing recursive trees with Python’s turtle graphics library is a fun way to explore recursion and fractal patterns. The code provided in this blog post demonstrates how to implement a recursive tree-drawing function using the turtle module. Feel free to modify the code and experiment with different angles, colors, and starting conditions to create unique and interesting tree visualizations.