fractal experimentationV0.2.py

""" For generating different looking fractals:  
cmap; supported values are 'Accent', 'Accent_r', 'Blues', 'Blues_r', 'BrBG', 'BrBG_r', 
'BuGn', 'BuGn_r', 'BuPu', 'BuPu_r', 'CMRmap', 'CMRmap_r', 'Dark2', 'Dark2_r', 'GnBu', 
'GnBu_r', 'Greens', 'Greens_r', 'Greys', 'Greys_r', 'OrRd', 'OrRd_r', 'Oranges', 
'Oranges_r', 'PRGn', 'PRGn_r', 'Paired', 'Paired_r', 'Pastel1', 'Pastel1_r', 
'Pastel2', 'Pastel2_r', 'PiYG', 'PiYG_r', 'PuBu', 'PuBuGn', 'PuBuGn_r', 
'PuBu_r', 'PuOr', 'PuOr_r', 'PuRd', 'PuRd_r', 'Purples', 'Purples_r', 
'RdBu', 'RdBu_r', 'RdGy', 'RdGy_r', 'RdPu', 'RdPu_r', 'RdYlBu', 'RdYlBu_r',
'RdYlGn', 'RdYlGn_r', 'Reds', 'Reds_r', 'Set1', 'Set1_r', 'Set2', 'Set2_r',
'Set3', 'Set3_r', 'Spectral', 'Spectral_r', 'Wistia', 'Wistia_r', 'YlGn',
'YlGnBu', 'YlGnBu_r', 'YlGn_r', 'YlOrBr', 'YlOrBr_r', 'YlOrRd', 'YlOrRd_r', 
'afmhot', 'afmhot_r', 'autumn', 'autumn_r', 'binary', 'binary_r', 'bone', 
'bone_r', 'brg', 'brg_r', 'bwr', 'bwr_r', 'cividis', 'cividis_r', 'cool',
'cool_r', 'coolwarm', 'coolwarm_r', 'copper', 'copper_r', 'cubehelix', 
'cubehelix_r', 'flag', 'flag_r', 'gist_earth', 'gist_earth_r',
'gist_gray', 'gist_gray_r', 'gist_heat', 'gist_heat_r', 'gist_ncar',
'gist_ncar_r', 'gist_rainbow', 'gist_rainbow_r', 'gist_stern', 
'gist_stern_r', 'gist_yarg', 'gist_yarg_r', 'gnuplot', 'gnuplot2',
'gnuplot2_r', 'gnuplot_r', 'gray', 'gray_r', 'hot', 'hot_r', 'hsv',
'hsv_r', 'inferno', 'inferno_r', 'jet', 'jet_r', 'magma', 'magma_r'
, 'nipy_spectral', 'nipy_spectral_r', 'ocean', 'ocean_r', 'pink', 
'pink_r', 'plasma', 'plasma_r', 'prism', 'prism_r', 'rainbow', 
'rainbow_r', 'seismic', 'seismic_r', 'spring', 'spring_r', 
'summer', 'summer_r', 'tab10', 'tab10_r', 'tab20', 'tab20_r', 
'tab20b', 'tab20b_r', 'tab20c', 'tab20c_r', 'terrain', 'terrain_r',
'turbo', 'turbo_r', 'twilight', 'twilight_r', 'twilight_shifted',
'twilight_shifted_r', 'viridis', 'viridis_r', 'winter', 'winter_r'
value for interpolation; supported values are 'antialiased', 'none', 'nearest', 
'bilinear', 'bicubic', 'spline16', 'spline36', 'hanning', 'hamming', 'hermite',
'kaiser', 'quadric', 'catrom', 'gaussian', 'bessel', 'mitchell', 'sinc', 'lanczos',
'blackman'
 """
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.animation as animation
from tqdm import tqdm
from datetime import date

x_start, y_start = -2, -2  # an interesting region starts here
width, height = 4, 4  # for 4 units up and right
density_per_unit = 700  # how many pixels per unit

# real and imaginary axis
re = np.linspace(x_start, x_start + width, width * density_per_unit)
im = np.linspace(y_start, y_start + height, height * density_per_unit)


threshold = 50  # max allowed iterations
frames = 23  # number of frames in the animation

# we represent c as c = r*cos(a) + i*r*sin(a) = r*e^{i*a}
r = 0.7885
a = np.linspace(0, 2 * np.pi, frames)

fig = plt.figure(figsize=(10, 10))  # instantiate a figure to draw
ax = plt.axes()  # create an axes object


def is_prime(n):
    """
    Check if a given number is prime or not.
    """
    if n <= 1:
        return False
    for i in range(2, int(n ** 0.5) + 1):
        if n % i == 0:
            return False
    return True


def julia_quadratic(z_re, z_im, c_re, c_im, threshold):
    """
    Generate a Julia set fractal based on prime numbers.
    """
    z = z_re + z_im * 1j
    c = c_re + c_im * 1j

    for i in range(threshold):
        if is_prime(abs(z)):
            return i
        z = z ** 2 + c

    return threshold


def animate(frame):
    ax.clear()  # clear axes object
    i = frame
    ax.set_xticks([], [])  # clear x-axis ticks
    X = np.empty((len(re), len(im)))  # the initial array-like image
    cx, cy = r * np.cos(a[i]), r * np.sin(a[i])  # the initial c number

    # iterations for the given threshold
    for i in tqdm(range(len(re))):
        for j in range(len(im)):
            X[i, j] = julia_quadratic(re[i], im[j], cx, cy, threshold)

    img = ax.imshow(X.T, cmap="Spectral", interpolation="antialiased")

    return [img]


anim = animation.FuncAnimation(fig, animate, frames=frames, interval=20, blit=True)

# save the animation
# anim.save(f'juliaPrimesFractal_{date.today()}.gif', writer='imagemagick')

import datetime

# Get the current date and time
now = datetime.datetime.now()

# Define the output file name with the date included
output_file_name = f'juliaPrimesFractal_{now:%Y-%m-%d_%H-%M-%S}.gif'

# Save the animation with the new output file name
anim.save(output_file_name, writer='imagemagick')