This question relates to Add a vector to a list of vectors whereas here I want to add list of vectors to list of vectors recursively. Given:
m = {{1, 0}, {0, 1}, {-1, 0}, {0, -1}}
k = m
Adding each vector of m to each vector of k is done by
k = Transpose[# + Transpose[m]] & /@ k
resulting in
{{{2, 0}, {1, 1}, {0, 0}, {1, -1}}, {{1, 1}, {0, 2}, {-1, 1}, {0,0}}, {{0, 0}, {-1, 1}, {-2, 0}, {-1, -1}}, {{1, -1}, {0,0}, {-1, -1}, {0, -2}}}
This is my new k and should go back into my code, so I can add the vectors m
to each element of this new k. The new result starts with {{{{3,0},{2,1},{1,0),{2,-1}}... I tried
Table[k = (Transpose[# + Transpose[m]] & /@ k), {i, 2}]
But it does not work and then I get too confused. Any idea for this tree-like structure?