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

preset = 1

saveFigure = True
markerSize = 0.01
markerStyle = "," # . - point; , - pixel
if preset == 1: # Cover the whole range [-2, 2]
  cInterval = (-2.1, 2.1)
  cResolution = 0.0005
  mapIterationCount = 500
  lastMapIterationCountToPlot = 500
  startingIterationValue = 0.5
  fileName = "TentMapOrbitDiag.png"
  yLim = (-1.1, 2.5)
elif preset == 2: # Zoom on the period-doubling bifurcation region
  cInterval = (0.99, 1.1)
  cResolution = 0.00002
  mapIterationCount = 500
  lastMapIterationCountToPlot = 500
  startingIterationValue = 0.5
  fileName = "TentMapOrbitDiag_BifurcZoom.png"
  yLim = (0.45, 0.54)
  
lims = np.zeros(mapIterationCount)

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

for c in np.arange(cInterval[0], cInterval[1], cResolution):
  lims[0] = startingIterationValue
  for i in xrange(mapIterationCount - 1):
    lims[i + 1] = c * min(lims[i], 1 - lims[i])
    
  biax.plot([c] * lastMapIterationCountToPlot,
            lims[(mapIterationCount - lastMapIterationCountToPlot):], "b.",
            markersize=markerSize,
            marker=markerStyle)

biax.set(xlabel="c", ylabel="x",
         title="Tent map - c * min(x, 1-x) - bifurcation diagram/orbit diagram" + "\n"
               "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()