Third time's the charm: a program to generate all the 4x4 mazes

points.p6

# bitstring; positions 0..11 correspond to vertical walls; 12..23 to horizontal;
# RAKUDO: can't do `0 x 24` here: RT #123602
my @old = "000000000000000000000000";

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

# 0..8 represent the nine internal corner points; 9 represents the outer wall
my @points =
    # vertical walls 0..11
    [0, 9], [1, 9], [2, 9],
    [0, 3], [1, 4], [2, 5],
    [3, 6], [4, 7], [5, 8],
    [6, 9], [7, 9], [8, 9],
    # horizontal walls 12..23
    [0, 9], [0, 1], [1, 2], [2, 9],
    [3, 9], [3, 4], [4, 5], [5, 9],
    [6, 9], [6, 7], [7, 8], [8, 9],
;

my %symmetries =
    id   => 0..23,
    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>,
    rot3 => +«<20 16 12 21 17 13 22 18 14 23 19 15 9 6 3 0 10 7 4 1 11 8 5 2>,
    flip => +«<9 10 11 6 7 8 3 4 5 0 1 2 20 21 22 23 16 17 18 19 12 13 14 15>,
    frt1 => +«<12 16 20 13 17 21 14 18 22 15 19 23 0 3 6 9 1 4 7 10 2 5 8 11>,
    frt2 => +«<2 1 0 5 4 3 8 7 6 11 10 9 15 14 13 12 19 18 17 16 23 22 21 20>,
    frt3 => +«<23 19 15 22 18 14 21 17 13 20 16 12 11 8 5 2 10 7 4 1 9 6 3 0>,
;

sub p($s, $n) { $s.substr($n, 1) }
sub ch($s, $n) { $s.substr(0, $n) ~ "1" ~ $s.substr($n + 1) }

for 1..9 {
    my %new;
    for @old -> $s {
        my @active = False xx 9, True;
        for ^24 -> $n {
            next unless p($s, $n);
            @active[@points[$n][0]] = True;
            @active[@points[$n][1]] = True;
        }
        for ^24 -> $n {
            next if p($s, $n);
            my @p = @points[$n].list;
            if @active[@p[0]] != @active[@p[1]] {
                my @w = ch($s, $n).comb;
                my $min = [min] (@w[%symmetries{$_}.list].join for %symmetries.keys);
                %new{$min}++;
            }
        }
    }

    @old = %new.keys;
    note +@old;
}

.say for @old.sort;

# real  14m39.795s
# user  14m37.898s
# sys   0m2.157s

This gist has bit-rotted just a skosh. Easy to fix; see my fork.

BTW, unique 3x4 rectangular mazes are in number 629.