In [3]:
from numpy import *
%matplotlib inline
import matplotlib.pyplot as plt
In [7]:
for b in linspace(0,4,26):
    x = 0.3
    plt.plot(b,x,'c.',alpha=0.1)
    for t in range(200):
        x = b*(1-x)*x
        plt.plot(b,x,'c.',alpha=0.1)
plt.show()
In [ ]:
for b in linspace(0,4,26):
    x = 0.3
    plt.plot(b,x,'c.',alpha=0.1)
    for t in range(200):
        x = b*(1-x)*x
        plt.plot(b,x,'c.',alpha=0.1)
plt.show()
In [8]:
linspace(0.5,0.5,10)
Out[8]:
array([ 0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5])
In [9]:
0.5*ones(10)
Out[9]:
array([ 0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5])
In [ ]:
b = linspace(0,4,501)
x = ones_like(b)
In [27]:
b = linspace(0,4,500)
x = 0.3*ones_like(b)
#print(x)
#print(b)
#plt.plot(b,x,'c.',alpha=0.1)
plt.figure(figsize=(15,5))
for t in range(200):
    x = b*(1-x)*x
    if t>150: plt.plot(b,x,'k.',alpha=0.2,markersize=1)
#plt.ylim(0,1)
plt.show()
In [32]:
#Focus on one b value
b = 2.1
x = 0.3
plt.plot(0,x,'ro')
for t in range(10):
    x = b*(1-x)*x
    plt.plot(t+1,x,'ro',clip_on=False)
In [38]:
#Focus on one b value
b = 3.1
x = 0.3
y = 0.300001
plt.subplot(2,1,1)
plt.plot(0,x,'ro')
for t in range(40):
    x = b*(1-x)*x
    y = b*(1-y)*y
    plt.subplot(2,1,1)
    plt.plot(t+1,x,'ro',clip_on=False,ms=10)
    plt.plot(t+1,y,'bo',clip_on=False,ms=5)
    plt.subplot(2,1,2)
    plt.plot(t+1,   )