Fayl:Logistic Map Bifurcation Diagram, Matplotlib.svg

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Qisqa izoh

Taʼrif
English: A bifurcation diagram for the Logistic map:
The horizontal axis is the r parameter, the vertical axis is the x variable. A starting value of x=0.25 was used, and the map was iterated 1000 times in order to stabilize the values of x. 1,000,000 x -values were then calculated for each value of r and for each x value, the corresponding (x,r) pixel in the image was incremented by one. All values in a column (corresponding to a particular value of r) were then multiplied by the number of non-zero pixels in that column, in order to even out the intensities. See File:Logistic Map Bifurcation Diagram, Matplotlib, zoomed.png for a vectorized and therefore much faster version of this Python script.
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Manba Oʻzimning ishim
Muallif Morn
SVG genesis
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 This plot was created with Matplotlib.
Source code
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Python code

Source code 
from pylab import *
from numpy import NaN
from matplotlib.colors import LogNorm

dr, dx = .001, .001
max_it = 1000000

R = arange(2.4, 4, dr)
X = arange(0, 1, dx)
Z = zeros((len(X), len(R)))

for ir, r in enumerate(R):
	print (ir, "of", len(R))
	z = .25
	for i in range(1000):
		z = r * z * (1 - z)
	for i in range(max_it):
		z = r * z * (1 - z)
		Z[-int(z / dx), ir] += 1
	Z[:, ir] *= count_nonzero(Z[:, ir])

Z = where(Z > 0, Z, NaN)
save("logmap", Z)	# save array to file

# pick color bar range:
zmi = .005 * nanmax(Z)
zma = .1   * nanmax(Z)

imshow(Z, cmap = plt.cm.viridis_r, vmin = zmi, vmax = zma,
  interpolation = 'none', norm = LogNorm(),
  extent = (R.min(), R.max(), X.min(), X.max()))
xlabel("r")
ylabel("x")
savefig("Logistic Map Bifurcation Diagram, Matplotlib.svg")
show()

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I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
atribut bir xil ulashish
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
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  • remiks qilishga – ishni moslashtirishga
Quyidagi shartlar asosida:
  • atribut – Siz tegishli litsenziyaga havolani taqdim etishingiz va oʻzgartirishlar kiritilganligini koʻrsatishingiz kerak. Siz buni har qanday oqilona yoʻl bilan qilishingiz mumkin, lekin litsenziar Sizni yoki Sizning foydalanishingizni ma'qullashini taklif qiladigan tarzda emas.
  • bir xil ulashish – Agar Siz materialni remiks qilsangiz, oʻzgartirsangiz yoki unga asoslansangiz, oʻz hissalaringizni asl nusxadagi kabi bir xil yoki mos litsenziya ostida tarqatishingiz kerak.
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tashkil etilgan

19 yanvar 2019

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joriy14:55, 2019-yil 19-yanvar14:55, 2019-yil 19-yanvar dagi versiya uchun tasvir576 × 432 (771 KB)wikimediacommons>Mornuse a million samples (less noise)

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