File:Folded towel map attractor, animated.gif
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[edit]DescriptionFolded towel map attractor, animated.gif |
English: ```python
import numpy as np def dynamical_system(x, y, z, a, b, n_iter): x_values = np.empty(n_iter) y_values = np.empty(n_iter) z_values = np.empty(n_iter) x_values[0] = x y_values[0] = y z_values[0] = z for i in range(1, n_iter): x, y, z = x_values[i], y_values[i], z_values[i] = a * x * (1 - x) - 0.05 * (y + 0.35) * (1 - 2 * z), 0.1 * ((y + 0.35) * (1 + 2 * z) - 1) * (1 - 1.9 * x), 3.78 * z * (1 - z) + b * y return x_values, y_values, z_values
a = 3.8 b = 0.2 x_init = 0.085 y_init = -0.121 z_init = 0.075 n_iter = 800000 x, y, z = dynamical_system(x_init, y_init, z_init, a, b, n_iter) init_time = 1000 def normalize(x): a, b = np.quantile(x, 0.999), np.quantile(x, 0.001) return 2 * (x - (a+b)/2) / (a - b) x = normalize(x)[init_time:] y = normalize(y)[init_time:] z = normalize(z)[init_time:] print(min(x), max(x), min(y), max(y), min(z), max(z)) %%capture import matplotlib.pyplot as plt import numpy as np import os for i, theta in enumerate( np.linspace(0, 2*np.pi, 120)): fig, ax = plt.subplots(figsize=(20, 20)) init_time = 1000 ax.scatter(y*np.cos(theta) + z*np.sin(theta), x, color='k', s=0.005) ax.axis("off") ax.set_xlim(-1.06, 1.06) ax.set_ylim(-1.03, 1.03) dir_path = f"./towel" if not os.path.exists(dir_path): os.makedirs(dir_path) fig.savefig(f"{dir_path}/{i}.png") plt.close() import imageio.v3 as iio import os from natsort import natsorted import moviepy.editor as mp for dir_path in ["./towel"]: file_names = natsorted((fn for fn in os.listdir(dir_path) if fn.endswith('.png'))) # Create a list of image files and set the frame rate images = [] fps = 12 # Iterate over the file names and append the images to the list for file_name in file_names: file_path = os.path.join(dir_path, file_name) images.append(iio.imread(file_path)) filename = dir_path[2:] iio.imwrite(f"{filename}.gif", images, duration=1000/fps, rewind=True) clip = mp.ImageSequenceClip(images, fps=fps) clip.write_videofile(f"{filename}.mp4")``` |
Date | |
Source | Own work |
Author | Cosmia Nebula |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 06:45, 25 April 2023 | 2,000 × 2,000 (71.77 MB) | Cosmia Nebula (talk | contribs) | Uploaded while editing "Hyperchaos" on en.wikipedia.org |
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