Seeing more detail from a graph of nonlinear equations

Question

I have a plot of isocontours for nonlinear system of functions and I I'm trying to get more detail in the graph. I know for sure that there are 3 more isocontour (island shapes) inside the iscontour(ring) labelled 1. These would be the local minimas. I do not quite understand how I can zoom further into the graph have them rendering in the diagram.

Quite new to python and Jupyter notebook, would appreciate any insight into how I might do this.

delta = 0.025
x = np.arange(-3, 1.0, delta)
y = np.arange(-3, 2.0, delta)
X, Y = np.meshgrid(x, y)
e1 = X*X + 2*Y*Y + np.sin(2*X)
e2 = X*X + np.cos(X+5*Y) - 1.2
Z = e1**2 + e2**2 

fig, ax = plt.subplots()
CS = ax.contour(X, Y, Z, np.array([1, 5, 10, 50, 100]))
ax.clabel(CS, inline=True, fontsize=10)

Current output

Answer 1

Well, if you know that there are three minima inside the contour of value 1, then you can give smaller values to the levels parameter to see them:

import matplotlib.pyplot as plt                                                                                       
import numpy as np                                                                                                    
                                                                                                                      
                                                                                                                      
delta = 0.025                                                                                                         
x = np.arange(-3, 1.0, delta)                                                                                         
y = np.arange(-3, 2.0, delta)                                                                                         
X, Y = np.meshgrid(x, y)                                                                                              
e1 = X*X + 2*Y*Y + np.sin(2*X)                                                                                        
e2 = X*X + np.cos(X+5*Y) - 1.2                                                                                        
Z = e1**2 + e2**2 # ensure's its positive                                                                             
                                                                                                                      
fig, ax = plt.subplots()                                                                                              
CS = ax.contour(X, Y, Z, np.array([0.1, 1, 5, 10, 50, 100]))                                                          
ax.clabel(CS, inline=True, fontsize=10)                                                                               
ax.set_xlim(-3, 1)                                                                                                    
ax.set_ylim(-2, 1)                                                                                                    
plt.show()                                                                                                            

You can also modify the centering of the axes by using xlim and ylim like I did above: if you make the box smaller, the three minima will be more visible.