A simple python script that generates custom epicycloidal figures frame by frame. (ffmpeg is required for the video generation)

epicycloid.py

import numpy as np
import matplotlib.pyplot as plt
import sys
import os
import platform
import subprocess

from progress.bar import IncrementalBar

def is_tool(name):
    try:
        devnull = open(os.devnull)
        subprocess.Popen([name], stdout=devnull, stderr=devnull).communicate()
    except OSError as e:
        if e.errno == os.errno.ENOENT:
            return False
    return True

def epicycloid_plotter(precision, n, k, path, dpi):
    X = np.cos(np.linspace(0, 2 * np.pi, precision))
    Y = np.sin(np.linspace(0, 2 * np.pi, precision))

    fig = plt.figure(figsize=(19.2, 14.4))
    plt.plot(X, Y, c="r")
    final = zip(X, Y)

    X_1 = np.cos(n * np.linspace(0, 2 * np.pi, precision))
    Y_1 = np.sin(n * np.linspace(0, 2 * np.pi, precision))
    final_1 = zip(X_1, Y_1)

    finale = zip(final, final_1)
    for i in finale:
        plt.plot([i[0][0], i[1][0]], [i[0][1], i[1][1]], c="r")

    plt.axis('equal')

    index = ""

    if k < 10:
        index = "000" + str(k)

    if k >= 10 and k < 100:
        index = "00" + str(k)

    if k >= 100 and k < 1000:
        index = "0" + str(k)

    plt.gca().get_xaxis().set_visible(False)
    plt.gca().get_yaxis().set_visible(False)

    ax = plt.gca()

    ax.spines['right'].set_visible(False)
    ax.spines['top'].set_visible(False)
    ax.spines['left'].set_visible(False)
    ax.spines['bottom'].set_visible(False)

    plt.savefig(
        os.path.join(path, "epycicloid" + index + ".png"),
        dpi=dpi,
        bbox_inches="tight",
        transparent=True,
    )

    plt.close()


k = 1

print("Insert the minimum value of n: ", end="")
n_min = int(input())

if n_min <= 0:
    print("The values of n cannot be negative or equal to zero")
    sys.exit()

print("Insert the maximum value of n: ", end="")
n_max = int(input())

if n_max <= 0:
    print("The values of n cannot be negative or equal to zero")
    sys.exit()

if n_min >= n_max:
    print("The minimum value of n cannot be greater or equal than the maximum value of n")
    sys.exit()

if n_max > 9999 or n_min > 9999:
    print("The values of n cannot be greater than 9999")
    sys.exit()

print("Insert the increment of n in each iteration: ", end="")
n_step = float(input())

if n_step <= 0:
    print("The increment of n cannot be negative or equal to zero")
    sys.exit()

print("Insert the precision of the plot: ", end="")
precision = int(input())

if precision <= 0:
    print("The precision cannot be negative or equal to zero")
    sys.exit()

print("Where do you want to save the images? (default: ./epycicloid/): ", end="")
path = input()

if path != "":
    if not os.path.exists(path):
        print("The path does not exist")
        sys.exit()  
else:
    path = "./epycicloid/"    

print("Insert the DPI value of the images (default: 300): ", end="")
dpi = input()

if dpi == "":
    dpi = 300
else:
    dpi = int(dpi)

if dpi <= 0:
    print("The DPI value cannot be negative or equal to zero")
    sys.exit()

bar = IncrementalBar('Generating images: ', max=int((n_max - n_min) / n_step))

for i in np.arange(n_min, n_max, n_step):
    epicycloid_plotter(precision, i, k, path, dpi)
    k += 1
    bar.next()

bar.finish()

print("Done! The images are saved in the folder: " + path)

print("Do you want to generate a video? (y/n) (default: y):", end="")
video = input()

if video == "n" or video == "N":
    sys.exit()
else:

    

    print("Insert the name of the video (default: epycicloid): ", end="")
    filename = input()

    print("Insert the video extension (default: mp4): ", end="")
    extension = input()

    if extension == "":
        extension = "mp4"

    if filename == "":
        filename = "epycicloid." + extension
    else:
        filename = filename + "." + extension

    print("Insert the FPS value of the video (default: 30): ", end="")
    fps = input()

    if fps == "":
        fps = 30
    else:
        fps = int(fps)

    #e.g. ffmpeg -i epycicloid%04d.png -r 20 -pix_fmt yuva420p outDark.webm
    os.system("ffmpeg -i " + path + "epycicloid%04d.png -r " + str(fps) + " -pix_fmt yuva420p " + filename)

    print("Done! The video is saved in the same folder of the images")

sys.exit()

requirements.txt

matplotlib==3.5.3
numpy==1.23.5
progress==1.6