SapinskiTraingle.py

# inspired from https://www.instagram.com/reel/Cl4WkH9OPXc/?igshid=YmMyMTA2M2Y%3D
from matplotlib import pyplot as plt
import numpy as np
import random
from math import sqrt

def plot_points(points):
    x = [p[0] for p in points]
    y = [p[1] for p in points]
    margin = 0.1
    maxx = max(x) + margin
    maxy = max(y) + margin
    minx = min(x) - margin
    miny = min(y) - margin
    # plt.rcParams['lines.markersize'] = 0.1
    plt.rcParams["figure.figsize"] = [18, 16]
    plt.rcParams["figure.autolayout"] = True
    plt.xlim(minx, maxx)
    plt.ylim(miny, maxy)
    plt.grid()
    s = [0.005] * len(x)
    plt.scatter(x, y, s=s, marker="o")
    plt.show()

def generate_points(triangle_points, first_point, num_to_generate):
    generated_points = [first_point]
    for idx in range(num_to_generate):
        selected_triangle_point = random.choice(triangle_points)
        last_generated_point = generated_points[-1]
        new_point = ((selected_triangle_point[0] + last_generated_point[0]) / 2, (selected_triangle_point[1] + last_generated_point[1]) / 2)
        generated_points.append(new_point)
    return generated_points

t1 = (0, 0)
t2 = (1, 0)
t3 = (1/2, sqrt(3) / 2)
first_point = (0.5 , 0.5)

generated_points = generate_points([t1, t2, t3], first_point, 1000000)
plot_points([t1, t2, t3] + generated_points)

This is the image generated from the code above