import numpy as np
import math
import matplotlib.pyplot as plt

preset = 5

markerSize = 0.001
saveFigure = True
markerStyle = "," # . - point; , - pixel
if preset == 1: # Diagram with positive c values in [0, 1]
  presetNote = "Initialize to 0\n; limit c to [0, 1] despite interesting patterns existing outside of it"
  presetNote = ""
  cInterval = (0, 1)
  cResolution = 0.0001
  mapIterationCount = 1000
  lastMapIterationCountToPlot = 1000
  startingIterationValue = 0.5
  fileName = "SineMapOrbitDiag.png"
  yLim = (0, 1)
if preset == 2: # Diagram with positive and negative c values
  presetNote = "Initialize to 0\n"
  cInterval = (-4, 4)
  cResolution = 0.001
  mapIterationCount = 500
  lastMapIterationCountToPlot = 500
  startingIterationValue = 0.5
  fileName = "SineMapOrbitDiag_BroadCRange.png"
  yLim = (-4, 4)
if preset == 3: # Diagram with positive and negative c values, larger interval
  presetNote = "Initialize to 0\n"
  cInterval = (-10, 10)
  cResolution = 0.002
  mapIterationCount = 500
  lastMapIterationCountToPlot = 500
  startingIterationValue = 0.5
  fileName = "SineMapOrbitDiag_BroadCRange2.png"
  yLim = (-10, 10)
if preset == 4: # Zoom on the bifurcation period doubling region
  presetNote = "Initialize to 0; zoom on the bifurcation period doubling region\n"
  cInterval = (0.84, 0.8657)
  cResolution = 0.000005
  mapIterationCount = 200
  lastMapIterationCountToPlot = 200
  startingIterationValue = 0.5
  fileName = "SineMapOrbitDiag_BifurcZoom.png"
  yLim = (0.3, 0.9)
if preset == 5: # Diagram with positive c values in [0, 1], init near zero
  presetNote = "Initialize to 1E-10 = near zero\n"
  cInterval = (0, 1)
  cResolution = 0.0001
  mapIterationCount = 500
  lastMapIterationCountToPlot = 500
  startingIterationValue = 1E-10
  fileName = "SineMapOrbitDiag_InitNearZero.png"
  yLim = (0, 1)
  
lims = np.zeros(mapIterationCount)

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

itemCount = 0
for c in np.arange(cInterval[0], cInterval[1], cResolution):
  itemCount += 1
  lims[0] = startingIterationValue
  for i in xrange(mapIterationCount - 1):
    lims[i + 1] = c * math.sin(math.pi * lims[i])
  if itemCount % 1000 == 0:
    print("Parameter values processed:", itemCount)

  biax.plot([c] * lastMapIterationCountToPlot,
            lims[(mapIterationCount - lastMapIterationCountToPlot):], "b.",
            markersize=markerSize,
            marker=markerStyle)

biax.set(xlabel="c", ylabel="x",
         title="Sine map - c * sin(pi * x) - bifurcation diagram/orbit diagram" + "\n" +
                presetNote +
               "c resolution: " + str(cResolution) +
               ", 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()