File:Logistic map approaching the period-3 scaling limit.webm
Original file (WebM audio/video file, VP9, length 12 s, 3,000 × 1,000 pixels, 594 kbps overall, file size: 835 KB)
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[edit]DescriptionLogistic map approaching the period-3 scaling limit.webm |
English: |
WEBM development InfoField | This plot was created with Matplotlib. |
Source code InfoField | Python codeimport numpy as np
import matplotlib.pyplot as plt
def logistic_map(x, r):
return r * x * (1 - x)
def function_iter(f, n, x, **kwargs):
for _ in range(n):
x = f(x, **kwargs)
return x
import imageio.v3 as iio
import os
from natsort import natsorted
import moviepy.editor as mp
def export_to_video(dir_paths, fps=12):
for dir_path in dir_paths:
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 = []
# 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")
return
from tqdm import tqdm
import os
r_min, r_max = 1+np.sqrt(8), 3.8494344
delta = 4.6692
frames_per_delta = 24
total_deltas = 6
frames = frames_per_delta * total_deltas
scaling_factor = delta**(1/frames_per_delta)
rs = r_max + (r_min - r_max) / (scaling_factor ** np.array(range(frames)))
for i, r in tqdm(enumerate(rs)):
highest_exponent = 8
fig, ax = plt.subplots(figsize=(30, 10))
x_min, x_max = 0.46, 0.54
x_values = np.linspace(x_min, x_max, 10000)
y_values = x_values
last_n_iter = 0
for n in range(highest_exponent):
n_iter = 3 * 2**n
y_values = function_iter(logistic_map, n_iter - last_n_iter, y_values, r=r)
last_n_iter = n_iter
ax.plot(x_values, y_values, label=f'iteration = {2**n}', alpha=0.2, color='blue')
ax.hlines(0.5, x_min, x_max, linewidth=0.3, alpha=0.8, linestyle='--', color='black')
# ax.legend()
ax.set_xlim(x_min, x_max)
ax.set_ylim(0.45, 0.53)
fig.suptitle(f'Up to {last_n_iter} iterates of the Logistic map with r = {r}',y=1.0)
plt.tight_layout()
dir_path = "./logistic_3"
if not os.path.exists(dir_path):
os.makedirs(dir_path)
fig.savefig(f"{dir_path}/{i}.png")
plt.close()
export_to_video(["./logistic_3"], fps=12)
|
Date | |
Source | Own work |
Author | Cosmia Nebula |
Licensing
[edit]This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. | |
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
http://creativecommons.org/publicdomain/zero/1.0/deed.enCC0Creative Commons Zero, Public Domain Dedicationfalsefalse |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 01:08, 7 April 2024 | 12 s, 3,000 × 1,000 (835 KB) | Cosmia Nebula (talk | contribs) | Uploaded own work with UploadWizard |
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