How to Create a Fractal Tree with Python’s Matplotlib and Recursion

We now use Python’s Matplotlib library to draw a fractal tree, employing iteration and recursion.

Import required libraries

import matplotlib.pyplot as plt
import math
import random

Define rotation angle

def rotate(x, y, angle):
    x_point = (x[0] + (math.cos(math.radians(angle))) * (x[1] - x[0])
               - math.sin(math.radians(angle)) * (y[1] - y[0]))
    y_point = (y[0] + math.sin(math.radians(angle)) * (x[1] - x[0])
               + math.cos(math.radians(angle)) * (y[1] - y[0]))
    return x_point, y_point

Calculate distance between two points

def distance(x, y):
    return math.sqrt((x[1] - x[0])**2 + (y[1] - y[0])**2)

Find split point

def find(x, y, d1, d2):
    ratio = d1 / d2
    n_x = (1 - ratio) * x[0] + ratio * x[1]
    n_y = (1 - ratio) * y[0] + ratio * y[1]
    return n_x, n_y

Draw recursive tree

def tree(x, y, count, angle, n):
    if count > 0:
        count -= 1
        dis = distance(x, y)
        plt.plot(x, y, linewidth=count + 1)
        d1 = dis + (dis / 2)
        n_x, n_y = find(x, y, d1, dis)
        x1, y1 = rotate([x[1], n_x], [y[1], n_y], angle)
        plt.plot([x[1], x1], [y[1], y1], linewidth=count)
        x2, y2 = rotate([x[1], n_x], [y[1], n_y], 0 - angle)
        plt.plot([x[1], x2], [y[1], y2], linewidth=count)
        tree([x[1], x1], [y[1], y1], count, angle, n)
        tree([x[1], x2], [y[1], y2], count, angle, n)
        plt.plot([x[1], n_x], [y[1], n_y], linewidth=count)
        tree([x[1], n_x], [y[1], n_y], count, angle, n)

x = [2, 2]
y = [0, 6]
angle = 45
tree(x, y, 6, angle, 3)
plt.show()

The resulting image shows a branching fractal tree.