Find all possible configurations of a finite dipole system

Question

I have a system which is composed of the following blocks
$$[-,+],[+,+],[+,-],[-,-]$$
I can compose a system of $n$ blocks with the only rule that the edges act as a dipole.
for example
$$[-,+][-,+][-,-][+,-]$$
is a possible configuration of $n=4$.
Is it possible to create a code with mathematica that will produce all the possible configurations for any given $n$?

Hausdorff · Accepted Answer

AttachDipole[x : {___, {_, "+"}}] := Append[x, #] & /@ {{"-", "-"}, {"-", "+"}};
AttachDipole[x : {___, {_, "-"}}] := Append[x, #] & /@ {{"+", "-"}, {"+", "+"}};

AttachDipoles[dipls_List] := Join @@ AttachDipole /@ dipls
AllDipoles[n_] := 
   Nest[AttachDipoles, {{{"-", "-"}}, {{"-", "+"}}, {{"+", "-"}}, {{"+", "+"}}}, n - 1]

AllDipoles[1]

{{{"-", "-"}}, {{"-", "+"}}, {{"+", "-"}}, {{"+", "+"}}}

AllDipoles[2]

{{{"-", "-"}, {"+", "-"}}, {{"-", "-"}, {"+", "+"}}, 
 {{"-", "+"}, {"-", "-"}}, {{"-", "+"}, {"-", "+"}}, 
 {{"+", "-"}, {"+", "-"}}, {{"+", "-"}, {"+", "+"}}, 
 {{"+", "+"}, {"-", "-"}}, {{"+", "+"}, {"-", "+"}}}

AllDipoles[3]

{{{"-", "-"}, {"+", "-"}, {"+", "-"}}, {{"-", "-"}, {"+", "-"}, {"+", "+"}}, 
 {{"-", "-"}, {"+", "+"}, {"-", "-"}}, {{"-", "-"}, {"+", "+"}, {"-", "+"}}, 
 {{"-", "+"}, {"-", "-"}, {"+", "-"}}, {{"-", "+"}, {"-", "-"}, {"+", "+"}}, 
 {{"-", "+"}, {"-", "+"}, {"-", "-"}}, {{"-", "+"}, {"-", "+"}, {"-", "+"}}, 
 {{"+", "-"}, {"+", "-"}, {"+", "-"}}, {{"+", "-"}, {"+", "-"}, {"+", "+"}}, 
 {{"+", "-"}, {"+", "+"}, {"-", "-"}}, {{"+", "-"}, {"+", "+"}, {"-", "+"}}, 
 {{"+", "+"}, {"-", "-"}, {"+", "-"}}, {{"+", "+"}, {"-", "-"}, {"+", "+"}}, 
 {{"+", "+"}, {"-", "+"}, {"-", "-"}}, {{"+", "+"}, {"-", "+"}, {"-", "+"}}}

Daniel Huber · Answer

Here is a one liner:
n = 3;
DeleteCases[Tuples[Tuples[{-1, 1}, 2],  n], {___, {_, x_}, {y_, _}, ___} /; ( x == y)]

{{{-1, -1}, {1, -1}, {1, -1}}, {{-1, -1}, {1, -1}, {1, 
   1}}, {{-1, -1}, {1, 1}, {-1, -1}}, {{-1, -1}, {1, 1}, {-1, 
   1}}, {{-1, 1}, {-1, -1}, {1, -1}}, {{-1, 1}, {-1, -1}, {1, 
   1}}, {{-1, 1}, {-1, 1}, {-1, -1}}, {{-1, 1}, {-1, 1}, {-1, 
   1}}, {{1, -1}, {1, -1}, {1, -1}}, {{1, -1}, {1, -1}, {1, 
   1}}, {{1, -1}, {1, 1}, {-1, -1}}, {{1, -1}, {1, 1}, {-1, 1}}, {{1, 
   1}, {-1, -1}, {1, -1}}, {{1, 1}, {-1, -1}, {1, 1}}, {{1, 1}, {-1, 
   1}, {-1, -1}}, {{1, 1}, {-1, 1}, {-1, 1}}}

Find all possible configurations of a finite dipole system

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