Why does this code for initializing a list of lists apparently link the lists together?

The problem is that they're all the same exact list in memory. When you use the [x]*n syntax, what you get is a list of n many x objects, but they're all references to the same object. They're not distinct instances, rather, just n references to the same instance.

To make a list of 3 different lists, do this:

x = [[] for i in range(3)]

This gives you 3 separate instances of [], which is what you want

[[]]*n is similar to

l = []
x = []
for i in range(n):
    x.append(l)

While [[] for i in range(3)] is similar to:

x = []
for i in range(n):
    x.append([])   # appending a new list!

In [20]: x = [[]] * 4

In [21]: [id(i) for i in x]
Out[21]: [164363948, 164363948, 164363948, 164363948] # same id()'s for each list,i.e same object


In [22]: x=[[] for i in range(4)]

In [23]: [id(i) for i in x]
Out[23]: [164382060, 164364140, 164363628, 164381292] #different id(), i.e unique objects this time