You were probably looking for something more complicated, but your step 3 is wrong. Your (2,2) is not 1, it is 109 (this is 1-based index, just like you did, simply to avoid more confusion).
Maybe what you are looking for is more like this:
use warnings;
use strict;
my @my_arr=(
[1, 11, 0, 0],
[12, 109, 0, 0],
[16, 1, 16, 0],
[14, 14, 2, 0],
[45, 16, 5, 4]
);
my ($index1, $index2) = (5, 4); #used 1-based index for easy communica
+tion
while (1) {
last if $index1 > 5 || $index1 < 1 || $index2 > 4 || $index2 < 1;
print $my_arr[$index1 - 1][$index2 - 1], "\n";
$index1 = $my_arr[$index1 - 1][$index2 - 1];
$index2 --;
}
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