sierpinski_gasket_fractals.py

import math
import time
import matplotlib.pyplot as plt

max_depth = 8

# Internal dividing point
m = 1
n = 1 

# Initial Conditions 
a0 = +0.0 + 0J
a1 = +1.0 + 0J
a2 = +0.5 + 1J*math.sqrt(3.0)/2.0

epsilon = 0.001
save_img_fname = "SierpinskiGasket_depth{}.png".format(max_depth)

def get_coordinate(triangle):
    x0 = triangle[0].real
    y0 = triangle[0].imag

    x1 = triangle[1].real
    y1 = triangle[1].imag

    x2 = triangle[2].real
    y2 = triangle[2].imag

    return (x0, y0), (x1, y1), (x2, y2)
    

def draw(triangles):
    plt.figure(figsize=(7, 7), dpi=150)
    print("drawing...")
    for triangle in triangles:
        (x0, y0), (x1, y1), (x2, y2) = get_coordinate(triangle)
        poly = plt.Polygon(((x0, y0), (x1, y1), (x2, y2)))
        plt.gca().add_patch(poly)
        
    plt.axis("off")
    plt.savefig(save_img_fname)
    print("{} has been saved".format(save_img_fname, max_depth))

def check_initial_conditions(a0, a1, a2):
    d0 = abs(a0-a1)
    d1 = abs(a1-a2)
    d2 = abs(a2-a0)
    if abs(d0-d1) > epsilon or abs(d1-d2) > epsilon or abs(d2-d0) > epsilon:
        print("initial condition is inccorect")

def make_3triangles_from_triangle(triangle):
    p0 = triangle[0]
    p1 = triangle[1]
    p2 = triangle[2]

    new_p2 = (m*p0 + n*p1) / (m+n)
    new_p0 = (m*p1 + n*p2) / (m+n)
    new_p1 = (m*p2 + n*p0) / (m+n)

    triangle0 = [p0, new_p1, new_p2]
    triangle1 = [new_p1, p2, new_p0]
    triangle2 = [new_p2, new_p0, p1]
    
    return triangle0, triangle1, triangle2 

def get_new_triangles(triangles):
    new_triangles = []
    for i, triangle in enumerate(triangles):
        triangle0, triangle1, triangle2 = make_3triangles_from_triangle(triangles[i])
        new_triangles.append(triangle0)
        new_triangles.append(triangle1)
        new_triangles.append(triangle2)

    return new_triangles

def get_circumference_and_area(triangles):
    distance_between_two_point = abs(triangles[-1][0] - triangles[-1][1])
    circumference = len(triangles) * distance_between_two_point
    area = math.sqrt(3)/4.0 * distance_between_two_point ** 2
    return circumference, area

def main():
    check_initial_conditions(a0,a1,a2)
    triangles = []
    triangles.append([a0, a1, a2])

    start = time.time() 
    for depth in range(max_depth):
        triangles = get_new_triangles(triangles)
        circumference, area = get_circumference_and_area(triangles)
        elapased_time = time.time() - start
        print("depth:{} num_triangles:{} circumference:{:.5f} area:{:.5f} time:{:.6f} [sec]".format(depth, len(triangles), circumference, area, elapased_time))

    start = time.time()
    draw(triangles)
    elapased_time = time.time() - start
    print("drowing time: {:.6f} [sec]".format(elapased_time))
    
if  __name__ == "__main__":
    main()

sierpinski_gasket_fractals_customized.py

import math
import time
import matplotlib.pyplot as plt

max_depth = 4

# Initial Conditions 
a0 = +0.0 + 0J
a1 = +1.0 + 0J
a2 = +0.5 + 1J*math.sqrt(3.0)/2.0

epsilon = 0.001
save_img_fname = "SierpinskiGasket_depth{}.png".format(max_depth)

def get_coordinate(triangle):
    x0 = triangle[0].real
    y0 = triangle[0].imag

    x1 = triangle[1].real
    y1 = triangle[1].imag

    x2 = triangle[2].real
    y2 = triangle[2].imag

    return (x0, y0), (x1, y1), (x2, y2)
    

def draw(triangles):
    plt.figure(figsize=(7, 7), dpi=150)
    print("drawing...")
    coordx = []
    coordy = []
    for triangle in triangles:
        (x0, y0), (x1, y1), (x2, y2) = get_coordinate(triangle)
        poly = plt.Polygon(((x0, y0), (x1, y1), (x2, y2)))
        plt.gca().add_patch(poly)
        
    plt.axis("off")
    plt.savefig(save_img_fname)
    plt.show()
    print("{} has been saved".format(save_img_fname, max_depth))

def check_initial_conditions(a0, a1, a2):
    d0 = abs(a0-a1)
    d1 = abs(a1-a2)
    d2 = abs(a2-a0)
    if abs(d0-d1) > epsilon or abs(d1-d2) > epsilon or abs(d2-d0) > epsilon:
        print("initial condition is inccorect")

def midpoint(p1, p2):
    return 2.0/3.0 * p1 + 1.0/3.0 * p2

def make_6triangles_from_triangle(triangle):
    p0 = triangle[0]
    p1 = triangle[1]
    p2 = triangle[2]

    new_p1 = midpoint(p0, p2) 
    new_p2 = midpoint(p2, p0)
    new_p3 = midpoint(p2, p1) 
    new_p4 = midpoint(p1, p2) 
    new_p5 = midpoint(p1, p0) 
    new_p6 = midpoint(p0, p1) 
    new_p0 = (new_p1 + new_p2 + new_p3 + new_p4 + new_p5 + new_p6) / 6.0 

    triangle0 = [p0, new_p6, new_p1]
    triangle1 = [new_p5, p1, new_p4]
    triangle2 = [new_p2, new_p3, p2]

    triangle3 = [new_p6, new_p5, new_p0]
    triangle4 = [new_p0, new_p4, new_p3]
    triangle5 = [new_p1, new_p0, new_p2]
    
    return triangle0, triangle1, triangle2, triangle3, triangle4, triangle5 

def get_new_triangles(triangles):
    new_triangles = []
    for i, triangle in enumerate(triangles):
        triangle0, triangle1, triangle2, triangle3, triangle4, triangle5 = make_6triangles_from_triangle(triangles[i])
        new_triangles.append(triangle0)
        new_triangles.append(triangle1)
        new_triangles.append(triangle2)
        new_triangles.append(triangle3)
        new_triangles.append(triangle4)
        new_triangles.append(triangle5)

    return new_triangles

def get_circumference_and_area(triangles):
    distance_between_two_point = abs(triangles[-1][0] - triangles[-1][1])
    circumference = len(triangles) * distance_between_two_point
    area = math.sqrt(3)/4.0 * distance_between_two_point ** 2
    return circumference, area

def main():
    check_initial_conditions(a0,a1,a2)
    triangles = []
    triangles.append([a0, a1, a2])

    start = time.time()
    for depth in range(max_depth):
        triangles = get_new_triangles(triangles)
        circumference, area = get_circumference_and_area(triangles)
        elapased_time = time.time() - start
        print("depth:{} num_triangles:{} circumference:{:.5f} area:{:.5f} time:{:.6f} [sec]".format(depth, len(triangles), circumference, area, elapased_time))

    start = time.time()
    draw(triangles)
    elapased_time = time.time() - start
    print("drowing time: {:.6f} [sec]".format(elapased_time))
    
if  __name__ == "__main__":
    m