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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