Script to classify symmetries in 4x4 mazes

classify-symmetries.p6

#   00  01  02
# 12  13  14  15
#   03  04  05
# 16  17  18  19
#   06  07  08
# 20  21  22  23
#   09  10  11

my %symmetries =
    rot1 => +«<15 19 23 14 18 22 13 17 21 12 16 20 2 5 8 11 1 4 7 10 0 3 6 9>,
    rot2 => +«<11 10 9 8 7 6 5 4 3 2 1 0 23 22 21 20 19 18 17 16 15 14 13 12>,
    horz => +«<2 1 0 5 4 3 8 7 6 11 10 9 15 14 13 12 19 18 17 16 23 22 21 20>,
    vert => +«<9 10 11 6 7 8 3 4 5 0 1 2 20 21 22 23 16 17 18 19 12 13 14 15>,
;

for lines() -> $line {
    my @w = $line.comb;
    my @symm;

    for %symmetries.keys -> $s {
        if @w[%symmetries{$s}.list].join eq $line {
            @symm.push: $s;
        }
    }

    say "$line\t@symm.join(' ')";
}

You might be interested in http://oeis.org/A007341
They give Maple code that computes 1x1, 2x2, up to 20x20, all in under a second. Doesn't track symmetries, though.

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