File:LogisticMapOrbitDiag BifurcZoom.png
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Original file (9,600 × 5,400 pixels, file size: 434 KB, MIME type: image/png)
Summary
| Description |
English: Produced by the following code adapted from code from Wikipedia article Logistic map:
import numpy as np
import matplotlib.pyplot as plt
preset = 3
saveFigure = True
markerSize = 0.001
markerStyle = "," # . - point; , - pixel
progressReportBlockLen = 1000
if preset == 1: # Complete diagram on the conventional range
rInterval = (-0.1, 4.1)
rResolution = 0.0005
mapIterationCount = 1000
lastMapIterationCountToPlot = 1000
startingIterationValue = 0.5
yLim = (-0.1, 1.1)
fileName = "LogisticMapOrbitDiag.png"
if preset == 2: # Complete diagram, including the negative r
rInterval = (-2.1, 4.1)
rResolution = 0.0005
mapIterationCount = 1000
lastMapIterationCountToPlot = 1000
startingIterationValue = 0.5
yLim = (-0.6, 1.6)
fileName = "LogisticMapOrbitDiag_InclNegR.png"
if preset == 3: # Zoom on the leftmost bifurcation region
rInterval = (3.54, 3.5705) #3.571
rResolution = 0.000004
mapIterationCount = 500 #1000
lastMapIterationCountToPlot = 500
startingIterationValue = 0.5
yLim = (0.33, 0.9)
fileName = "LogisticMapOrbitDiag_BifurcZoom.png"
if preset == 4: # Complete diagram on the conventional range, skip early iterates
rInterval = (-0.1, 4.1)
rResolution = 0.0005
mapIterationCount = 10000
lastMapIterationCountToPlot = 1000
startingIterationValue = 0.5
yLim = (-0.1, 1.1)
fileName = "LogisticMapOrbitDiag_SkipEarlyIter.png"
progressReportBlockLen = 100
lims = np.zeros(mapIterationCount)
fig, biax = plt.subplots()
fig.set_size_inches(16, 9)
itemCount = 0
for r in np.arange(rInterval[0], rInterval[1], rResolution):
itemCount += 1
lims[0] = startingIterationValue
for i in xrange(mapIterationCount - 1):
lims[i + 1] = r * lims[i] * (1 - lims[i])
if itemCount % progressReportBlockLen == 0:
print("Parameter values processed:", itemCount)
biax.plot([r] * lastMapIterationCountToPlot,
lims[(mapIterationCount - lastMapIterationCountToPlot):], "b.",
markersize=markerSize,
marker=markerStyle)
biax.set(xlabel="c", ylabel="x",
title="Logistic map - r * x (1 - x) - bifurcation diagram/orbit diagram" + "\n"
"r resolution: " + str(rResolution) +
", iteration count: " + str(mapIterationCount) +
", last values to plot count: " + str(lastMapIterationCountToPlot))
biax.set_ylim(yLim[0], yLim[1])
if saveFigure:
plt.savefig(fileName, dpi=600)
else:
plt.show()
|
| Date | |
| Source | Own work |
| Author | Dan Polansky |
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution 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.
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 11:16, 9 February 2024 | | 9,600 × 5,400 (434 KB) | wikimediacommons>Dan Polansky | Focus closer on the plotted lines |
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