How to create a list of mutable matrices from a cycle in python?

Question

My goal is to make a dynamic simulation. For that, I create a list of 2D matrices. Each matrix is supposed to change an entry at a time (a "time" instant is each step of the list, which is iterable).

I use this format because I want to use this list of matrices (that I create with Python) in Mathematica, to visualize the dynamics using the "Manipulate" function.

n=3 
M=[[0,0,0][0,1,0][0,0,0]]    # initial matrix M (a simple example)
l=[M]
numbersteps=10
for step in range(1,numbersteps+1):    

    for v1 in range(1,n**2+1):   
        for v2 in range(1,n**2+1):


            i=VertexIndex (M,v1)[0]    # i,j, ki, kj are indexes,
            j=VertexIndex (M,v1)[1]    # which I calculate in the function VertexIndex
            ki=VertexIndex (M,v2)[0]   # VertexIndex returns (int1,int2)
            kj=VertexIndex (M,v2)[1]


            if M[i-1][j-1]==1:  
                M[i-1][j-1]=-1
                M[ki-1][kj-1]=1     # changes the entry M(ki, kj)




    l.append(M)     # list of each matrix M, for each step 

I was expecting to get

l=[M(step1),M(step2),M(step3),...]`

Because M is changing its entries, I would see the dynamics when I run the sequence of different M's. But what I got was simply a list of the final matrix M, "numbersteps" times, i.e.,

l=[M(finalstep),M(finalstep),M(finalstep),...], such that len(l)=numbersteps.

Does this make sense? Where is my mistake? I appreciate any help.

Answer 1

The object M is created only once during its initialization, so each time you append M to l with l.append(M), you're appending a reference to the same object for each iteration, so as the object mutates, the values of all references to this object change as well.

You can instead append a deep copy of the list of lists (add from copy import deepcopy first):

l.append(deepcopy(M))