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File:Logistic Map Bifurcation Diagram, Matplotlib.svg

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Summary

Description
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.
Date
Source Own work
Author Morn
SVG development
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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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19 January 2019

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Date/TimeThumbnailDimensionsUserComment
current13:55, 19 January 2019Thumbnail for version as of 13:55, 19 January 2019576 × 432 (771 KB)Mornuse a million samples (less noise)
12:45, 19 January 2019Thumbnail for version as of 12:45, 19 January 2019576 × 432 (979 KB)MornUser created page with UploadWizard

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