calculating logistic map in real time misses many results - loops

Question

Many code examples of calculating the logistic map function
use arrays. For example
%matplotlib notebook
import numpy as np
import matplotlib.pyplot as plt
def logistic(r, x):
return r * x * (1 - x)
n = 1000
r = np.linspace(2.5, 4., n)
iterations = 1000
last = 900
x = 1e-5 * np.ones(n)
fig, ax1 = plt.subplots(figsize=(8, 8))
for i in range(iterations):
x = logistic(r, x)
if i >= (iterations - last):
ax1.plot(r, x, ',k', alpha=.25)
ax1.set_xlim(2.5, 4)
ax1.set_title("Bifurcation diagram")
This is the result:
However, I am trying to make real time plot of the function. My attempt results in many values being omitted.
import ipywidgets as widgets
%matplotlib notebook
import numpy as np
import matplotlib.pyplot as plt
def logistic(r, s):
return r * s * (1 - s)
fig = plt.figure()
ax = fig.add_subplot(111)
plt.ion()
fig.show()
fig.canvas.draw()
#j goes from 2.5 to 4
for j in [float(j) / 100 for j in range(250, 400, 1)]:
x=0.2
# for a given value of j, iterate the logistic function 1000x
for i in range(1000):
y=logistic(j, x)
x=y
#plot the iterated logistic function for a given value of j
ax.plot(j,y,'ko',markersize=1)
fig.canvas.draw()
It looks really bad.
It seems half the data is missing and the data points for larger values of r appear sparse. How can I iterate the logistic function to obtain all the values for a given r?

Answer 1

I figured it out. Basically, the logistic map 'explodes' and becomes chaotic only after it is iterated a few times. So, I have to iterate a few times 'silently' (to allow the function to converge if it will) and then to print out the next few iterated values like so.
import ipywidgets as widgets
%matplotlib notebook
import numpy as np
import matplotlib.pyplot as plt
import time
def logistic(r, s):
return r * s * (1 - s)
fig = plt.figure()
ax = fig.add_subplot(111)
plt.ion()
fig.show()
fig.canvas.draw()
#j goes from 2.5 to 4
j=2.5
#for j in [float(j) / 500 for j in range(1250, 2000, 1)]:
while j<4:
x=0.2
# for a given value of j, iterate the logistic function 1000x
for i in range(30):
y=logistic(j, x)
x=y
for i in range(50):
y=logistic(j, x)
ax.plot(j,y,'ko',markersize=.2)
x=y
#plot the iterated logistic function for a given value of j
fig.canvas.draw()
j=j+.01
which gives