File:LogisticMapOrbitDiag InclNegR.png

English: Created using the following code adapted from code from Wikipedia Logistic map article:

import numpy as np
import matplotlib.pyplot as plt

preset = 1
if preset == 1: # Complete diagram, including the negative r
  saveFigure = True
  markerSize = 0.001
  markerStyle = "," # . - point; , - pixel
  rInterval = (-2.1, 4)
  rResolution = 0.0005
  mapIterationCount = 1000
  lastMapIterationCountToPlot = 1000
  startingIterationValue = 0.5
  fileName = "LogisticMapOrbitDiag_InclNegR.png"

yLim = (-0.6, 1.6)

lims = np.zeros(mapIterationCount)

fig, biax = plt.subplots()
fig.set_size_inches(16, 9)

for r in np.arange(rInterval[0], rInterval[1], rResolution):
  lims[0] = startingIterationValue
  for i in xrange(mapIterationCount - 1):
    lims[i + 1] = r * lims[i] * (1 - lims[i])

  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()