In Python, copying objects is common, and a lot of “why did both variables change?” bugs come from mixing up three different operations: assignment, shallow copy, and deep copy.

Among assignment (=), shallow copy (copy), and deep copy (deepcopy), the most confusing part is usually not assignment vs. copy, but whether a shallow copy still shares nested mutable objects.

Assignment does not copy an object. It only binds another variable name to the same object. Because of that, changes seen through one variable are still changes to the same underlying object.

A shallow copy duplicates the outer container, but nested mutable objects may still be shared. A deep copy recursively duplicates nested objects too, so it is usually more isolated.

A practical rule of thumb is:

• Use assignment when you only want another name for the same object.
• Use shallow copy when copying the outer container is enough.
• Use deep copy when nested lists or dictionaries also need to be independent.

Below is a practical code example illustrating the differences among the three.

The butterfly curve, discovered by Temple H. Fay, is a beautiful curve that can be expressed using a polar coordinate function. Because of its elegance, I wanted to use it as my blog’s favicon.ico. Here, I’ll use Python’s matplotlib.pyplot package to draw the desired butterfly curve. First, let’s admire the beautiful butterfly curve.

1. First, We Need to Define the Mathematical Expression of the Butterfly Curve

It can also be expressed using spherical coordinates:

2. Choosing matplotlib.pyplot as the Plotting Tool in Python

1. First, import the necessary Python packages

import numpy as np
import matplotlib.pyplot as plt

2. Set the parameter values

t = np.arange(0.0, 12*np.pi, 0.01)
x = np.sin(t)*(np.e**np.cos(t) - 2*np.cos(4*t)-np.sin(t/12)**5)
y = np.cos(t)*(np.e**np.cos(t) - 2*np.cos(4*t)-np.sin(t/12)**5)

3. According to the formula, use numpy functions with plt to draw the required image

plt.figure(figsize=(8,6))
plt.axis('off')
plt.plot(x,y,color='blue',linewidth = '2')
#plt.show()
plt.savefig("butter.jpg",dpi=400)

4. Use Pillow to resize the image to an appropriate size for a favicon

from PIL import Image
im = Image.open("butter.jpg")
favicon = im.resize((50,50))
favicon.save("favicon.ico")