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Summary
| Description | Feigenbaum Tree from Logistic Map. For higher resolution: click here! |
| Date | |
| Source | Own work |
| Author | Damodar Rajbhandari |
Source code in Python 3.x (in Jupyter Notebook)
# Author: Damodar Rajbhandari (2023)
%reset -f
%matplotlib notebook
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import rc
from matplotlib.animation import FuncAnimation
from IPython.display import clear_output
from IPython.display import Image
plt.rcParams.update({
"text.usetex": True,
"font.family": "Computer Modern Roman",
"font.size": 24,
})
n_dots = 1_000_000 # total number of dots
k = np.linspace(0.0, 4.0, n_dots)
iterations = 100
fig = plt.figure(figsize=(20, 15))
ax = plt.axes()
ax.set_xlim(0.0, 4.0)
ax.set_ylim(0.0, 1.0)
rc('animation', html='html5')
def animate(i):
plt.cla()
ax.set_title(r"Feigenbaum Tree; $x^{(k)}_{n + 1} = k x^{(k)}_{n}(1 - x^{(k)}_{n})$ for $n= $"+" {}".format(i +1))
x = np.random.uniform(0.0, 1.0, n_dots)
for _ in range(i + 1):
x = k * x * (1 - x)
ax.plot(k, x, '.k', markersize=.04)
ax.set(xlabel=r'$k$', ylabel=r'$x^{(k)}_{n}$')
print("Done iteration = {}".format(i))
clear_output(wait=True)
fig = FuncAnimation(fig, animate, frames=iterations, interval=300, blit=True)
fig.save('feigenbaum_tree.gif', writer='imagemagick', fps=10)
with open('feigenbaum_tree.gif','rb') as f:
display(Image(data=f.read(), format='png'))
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 03:52, 9 February 2023 | | 400 × 400 (500 KB) | Drhere | reduced weightxheight to 400x400 |
| 03:40, 9 February 2023 |  | 2,000 × 1,500 (4.66 MB) | Drhere | compressed the file size | |
| 16:08, 8 February 2023 |  | 2,000 × 1,500 (10.57 MB) | Drhere | Uploaded own work with UploadWizard |
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