Why do I get an empty plot while using matplotlib?

Question

I was trying to create a bifurcation diagram using pyplot in Python 3. I first defined a function for the logistic map and then used it in a second function in a for loop to generate the bifurcation diagram. The following is my code:

import numpy as np
import matplotlib.pyplot as plt

def logistic(n, r, x0):
    xn = []
    for i in range(1,n+1):
        x0 = r*x0*(1-x0)
        xn += [x0]
        xn = np.array(xn)
        return xn
        
def bifurcation(n, k, rmin, rmax, rstep, x0):
    for r in np.arange(rmin, rmax, rstep):
        traj = logistic(n, r, x0)
        R = r*np.ones([1, n+1])
        plt.scatter(R[k:n], traj[k:n])
    plt.xlim([rmin, rmax])
    plt.ylim([0, 1])
    plt.show()

bifurcation(50, 5, 2.4, 4, 0.1, 0.2)

The problem is that I get a blank plot as the output. No points are plotted at all. What am I doing wrong here?

Answer 1

import numpy as np
import matplotlib.pyplot as plt

def logistic(n, r, x0):
    xn = []
    for i in range(1,n+1):
        x0 = r*x0*(1-x0)
        xn += [x0]

    xn = np.array(xn)
    #print(xn.shape)
    return xn
        
def bifurcation(n, k, rmin, rmax, rstep, x0):
    for r in np.arange(rmin, rmax, rstep):
        traj = logistic(n, r, x0)
        R = r*np.ones(shape=n)
        plt.scatter(R[k:n], traj[k:n])
        #print(R.shape)

    plt.xlim([rmin, rmax])
    plt.ylim([0, 1])
    plt.show()

bifurcation(50, 5, 2.4, 4, 0.1, 0.2)

you forgot tabs in logistic() and np.ones vas a bit strange

Answer 2

When I first ran your code, I noticed that R[k:n] and traj[k:n] were both empty. It turns out that you've defined R such that there is a list inside of a list, and it's the inner list that has the numbers.

Thus, I just grabbed the inner list rather than using the outer one. So R = r*np.ones([1, n+1]) became R = r*np.ones([1, n+1])[0] . (There may be a more elegant way of doing this, but this should suffice.)

Then, for traj , it looks like traj only computes a single number (and puts it inside of a list), but in order to graph information, you need to have each of the x and y lists for the scatter function to have the right size. So I just duplicated the single number as many times as needed ( nk times). So traj[k:n] should instead be [traj[0]] * (nk) .

And then we get a graph:

Here's the full code:

import numpy as np
import matplotlib.pyplot as plt

def logistic(n, r, x0):
    xn = []
    for i in range(1,n+1):
        x0 = r*x0*(1-x0)
        xn += [x0]
        xn = np.array(xn)
        return xn

def bifurcation(n, k, rmin, rmax, rstep, x0):
    for r in np.arange(rmin, rmax, rstep):
        traj = logistic(n, r, x0)
        R = r*np.ones([1, n+1])[0]
        R_list = R[k:n]
        traj_list = [traj[0]] * (n-k)
        plt.scatter(R_list, traj_list)
    plt.xlim([rmin, rmax])
    plt.ylim([0, 1])
    plt.show()

bifurcation(50, 5, 2.4, 4, 0.1, 0.2)

Not sure if this is what you were looking for, but it seems to solve your problem of not getting a graph to show up. Hopefully it's helpful.