Fractal tree pattern plot using python

 

import matplotlib.pyplot as plt

import numpy as np

def draw_branch(ax, x, y, length, angle, depth, branch_factor=0.7, angle_variation=30):

    if depth == 0:

        return

    new_x = x + length * np.cos(np.radians(angle))

    new_y = y + length * np.sin(np.radians(angle))

    ax.plot([x, new_x], [y, new_y], 'brown', lw=depth)

    draw_branch(ax, new_x, new_y, length * branch_factor, angle + angle_variation, depth - 1)

    draw_branch(ax, new_x, new_y, length * branch_factor, angle - angle_variation, depth - 1)

def fractal_tree():

    fig, ax = plt.subplots(figsize=(8, 8))

    ax.set_xticks([])

    ax.set_yticks([])

    ax.set_frame_on(False)

    draw_branch(ax, 0, -1, 1, 90, depth=10)

    plt.xlim(-1, 1)

    plt.ylim(-1, 1.5)

    plt.title('Fractal tree pattern plot')

    plt.show()

fractal_tree()

#source code --> clcoding.com 

Code Explanation:

1. Importing Required Libraries

import matplotlib.pyplot as plt

import numpy as np

matplotlib.pyplot: Used to plot the fractal tree.

numpy: Used for mathematical operations like cos and sin (for angle calculations).

2. Recursive Function to Draw Branches

def draw_branch(ax, x, y, length, angle, depth, branch_factor=0.7, angle_variation=30):

This function draws branches recursively.

Parameters:

ax: The matplotlib axis for plotting.

(x, y): The starting coordinates of the branch.

length: The length of the current branch.

angle: The angle at which the branch grows.

depth: The recursion depth, representing how many branch levels to draw.

branch_factor: Determines how much shorter each successive branch is.

angle_variation: Determines how much the new branches deviate from the main branch.

3. Base Condition (Stopping Recursion)

if depth == 0:

    return

When depth == 0, recursion stops, meaning the smallest branches are reached.

4. Calculating the New Branch Endpoints

new_x = x + length * np.cos(np.radians(angle))

new_y = y + length * np.sin(np.radians(angle))

Uses trigonometry to compute the (x, y) coordinates of the new branch:

cos(angle): Determines the horizontal displacement.

sin(angle): Determines the vertical displacement.

np.radians(angle): Converts degrees to radians.

5. Drawing the Branch

ax.plot([x, new_x], [y, new_y], 'brown', lw=depth)

The branch is drawn as a brown line.

lw=depth: Line width decreases as depth decreases (thicker at the bottom, thinner at the tips).

6. Recursively Creating Two New Branches

draw_branch(ax, new_x, new_y, length * branch_factor, angle + angle_variation, depth - 1)

draw_branch(ax, new_x, new_y, length * branch_factor, angle - angle_variation, depth - 1)

Two smaller branches sprout from the current branch at:

angle + angle_variation (left branch).

angle - angle_variation (right branch).

Each new branch has:

A reduced length (length * branch_factor).

One less depth (depth - 1).

7. Creating the Fractal Tree

def fractal_tree():

    fig, ax = plt.subplots(figsize=(8, 8))

    ax.set_xticks([])

    ax.set_yticks([])

    ax.set_frame_on(False)

Creates a figure and axis for plotting.

Removes ticks (set_xticks([]), set_yticks([])) and frame (set_frame_on(False)) for a clean look.

8. Calling the Recursive Function

draw_branch(ax, 0, -1, 1, 90, depth=10)

Starts drawing the tree at (0, -1), which is near the bottom center.

The initial branch:

Length = 1

Angle = 90° (straight up)

Depth = 10 (controls the number of branch levels).

9. Setting Plot Limits & Displaying the Tree

plt.xlim(-1, 1)

plt.ylim(-1, 1.5)

plt.title('Fractal tree pattern plot')

plt.show()

Limits the x-axis (-1 to 1) and y-axis (-1 to 1.5) to keep the tree centered.

Displays the fractal tree with plt.show().