File:LogisticMapOrbitDiag P3Zoom.png

import numpy as np
import matplotlib.pyplot as plt

preset = 5

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
if preset == 5: # Zoom into the period-3 window
  rInterval = (3.825, 3.865)
  rResolution = 0.000005
  mapIterationCount = 1000
  lastMapIterationCountToPlot = 1000
  startingIterationValue = 0.5
  yLim = (0.1, 1.0)
  fileName = "LogisticMapOrbitDiag_P3Zoom.png"
  
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()