Trying to create and alter grid, but assigning values to specific index in nested list is unexpectedly duplicated to other nested lists

(Python 3.9) I'm trying to solve a percolation problem/assignment, and just to start, I'm creating an n-by-n grid. While the grid looks correct on creation, when I try to alter a specific value inside the grid (in a nested list), it's assigning that value to every sublist, rather than only the list I'm referencing with it's index.

Here's the class and relevant bits:

class Percolation:
    """Create an n-by-n grid, with all sites initially blocked."""
    def __init__(self, n):
        self.grid = self.create_grid(n)

    def create_grid(self, n):
        """ Create n-by-n grid with default 0 (blocked) values."""
        grid = []
        # Create x, rows.
        values = [0 for _ in range(n)]
        # Create y, columns.
        for _ in range(n):
            grid.append(values)
        return grid

    def show_grid(self):
        for row in self.grid:
            print(row)

size = 5
perc = Percolation(size)
# I chose 8 and 5 arbitrarily to test this issue so they're easy to spot.
perc.grid[0][2] = 8
perc.grid[1][1] = 5
perc.show_grid()

show_grid() is then showing me all sublists are changed.

>>> 
[0, 5, 8, 0, 0]
[0, 5, 8, 0, 0]
[0, 5, 8, 0, 0]
[0, 5, 8, 0, 0]
[0, 5, 8, 0, 0]

While what I was expecting is this:

>>> 
[0, 0, 8, 0, 0]
[0, 5, 0, 0, 0]
[0, 0, 0, 0, 0]
[0, 0, 0, 0, 0]
[0, 0, 0, 0, 0]

Am I making the mistake when I create the grid by appending "values" multiple times in a loop? Or am I incorrectly referencing indexes? I thought maybe at first show_grid() was accidentally printing the same row over and over, but printing self.grid directly still shows duplicate values across all sublists, regardless of n or how I assign values.

What I do see is that when I change only a value in the main list, I do get what I expect.

perc.grid[2] = [0, 0, 8, 0, 0]
perc.show_grid()

>>>
[0, 0, 0, 0, 0]
[0, 0, 0, 0, 0]
[0, 0, 8, 0, 0]
[0, 0, 0, 0, 0]
[0, 0, 0, 0, 0]

How do I properly change values in these nested lists in this case? What is actually happening when I'm setting perc.grid[0][2] = 8?