r=3.8
list_of_fX=[0.4]
for count in range(30):
    list_of_fX.append(r*list_of_fX[count]*(1-list_of_fX[count]))
plot1=list_plot(list_of_fX,plotjoined=true, axes_labels=["count ", "f(X)"])
show(plot1)

r=3.801
list_of_X_N=[0.4]
for count in range(30):
    list_of_X_N.append(r*list_of_X_N[count]*(1-list_of_X_N[count]))
plot2=list_plot(list_of_X_N,plotjoined=true, axes_labels=["count ", "X_N"], color="red")
show(plot1+plot2)

def discrete_logistic_difference(r, ics):
    list_of_fX=[ics]
    list_of_fX2=[ics+0.001]
    list_of_difference=[]
    for count in range(8):
        list_of_fX.append(r*list_of_fX[count]*(1-list_of_fX[count]))
        list_of_fX2.append(r*list_of_fX2[count]*(1-list_of_fX2[count]))
        list_of_difference.append(abs(r*list_of_fX[count]*(1-list_of_fX[count])-r*list_of_fX2[count]*(1-list_of_fX2[count])))
    return list_plot(list_of_difference,plotjoined=true, axes_labels=["count ", "difference"])

discrete_logistic_difference(3.8, 0.4)

r=3.8
list_of_fX=[0.4]
for count in range(300):
    list_of_fX.append(r*list_of_fX[count]*(1-list_of_fX[count]))

list_of_fX2=list_of_fX[100:]
list_of_points=list(zip([r]*150, list_of_fX2))
print(list_of_points)

list_of_r=srange(2.0, 4.0, 0.01)
master_list=[]

for r in list_of_r:
    list_of_X=[0.4]
    for count in range(250):
        list_of_X.append(r*list_of_X[count]*(1-list_of_X[count]))
    list_of_newX=list_of_X[100:]
    list_of_points=list(zip([r]*150, list_of_newX))
    master_list=master_list+list_of_points
print(master_list)