import numpy as np
import matplotlib.pyplot as plt

print "Mapeo Logistico"

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


r0 = 3.3; x0= 0.2
Nsteps = 50
xevolution = []
xcob= []
xnewcob= []
xevolution.append(x0)
xcob.append(x0)
xnewcob.append(0)

for i in range(Nsteps):
    xn = xevolution[-1]
    xnp1 = mlog(xn,r0)
    xevolution.append(xnp1)
    xnewcob.append(xn)
    xnewcob.append(xnp1)
    xcob.append(xnp1)
    xcob.append(xnp1)
    print i,xnp1

plt.ion()
plt.figure()
plt.title("r="+str(r0))
plt.xlabel(r"$t$")
plt.ylabel(r"$x_n$")
plt.plot(xevolution,'ro-')
plt.savefig('timeseries'+str(r0)+'.png',dpi=100)
plt.show()

plt.figure()
plt.title("r="+str(r0))
plt.xlabel(r"$x_n$")
plt.ylabel(r"$x_{n+1}$")
eje = np.linspace(0,1,100)
curva = [mlog(x,r0) for x in eje]
plt.plot(eje,curva,"k-")
plt.plot(eje,eje,"k-")
plt.plot(xnewcob[1:],xcob[1:],'ro-')
plt.savefig('cobweb'+str(r0)+'.png',dpi=100)
plt.show()