# logCobweb.py
# input: 2.5 or 3.2 or 3.5 or 3.56 or 3.84 or 4

'''
# https://ipython-books.github.io/121-plotting-the-bifurcation-diagram-of-a-chaotic-dynamical-system/

# Chaos and Fractals", David Feldman, Ch. 9
'''


import matplotlib.pyplot as plt
from frange import *


EPS = 0.0001
MAX_ORBITS = 100

def logistic(r, x):
  return r * x * (1 - x)



r = float(input("r? "))

fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 6))

ts = linspace(0, 1)

# Plot the logistic function in ax1
vals = [logistic(r, t) for t in ts]
ax1.plot(ts, vals, 'k', lw=2)
ax1.plot([0, 1], [0, 1])  # add the y=x line

x =  0.1
xs = [x]
prevX = 1000 # dummy 
i = 0
while (i < MAX_ORBITS) and (abs(x-prevX) > EPS):
  # print(i, f"{x:0.3f}")
  y = logistic(r, x)

  # plot lines between fn and y=x:
  ax1.plot([x, x], [x, y], 'k', ls='dashed') # vertical
  ax1.plot([x, y], [y, y], 'k', ls='dashed') # horizontal
  ax1.plot([x], [y], 'or', ms=5) # intersection pt
  prevX = x
  x = y
  xs.append(x)
  i += 1

ax1.set_xlim(0, 1)
ax1.set_ylim(0, 1)
ax1.set_xlabel("x_n")
ax1.set_ylabel("x_n+1")
ax1.set_title(f"Logistic map (r={r:.4f})")

# ----------------

# Plot changes of x values
tms = [t for t in range(len(xs))]
ax2.plot(tms, xs, 'bo-')
ax2.set_xlabel("n")
ax2.set_ylabel("x_n")
ax2.set_title("Time Series for x_n")

plt.show()