A search can be a simple grep:

my @found_nodes= grep { $_->value =~ /LookForThis/  } $tree->traverse(
+ $tree->POST_ORDER );
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Why do you want to avoid recursion? Performance reasons? Spec from instructor? Usually when people ask this sort of thing, it's an XY Problem.

As Anonymous Monk cheerfully points out, recursion is just iteration. This is usually most easily done with Loop Control. If your tree isn't doubly linked, you'll probably also want to maintain a stack for traversing upwards. Recursion is usually taught first because it is more intuitive. If you share your implemented binary tree (wrapped in code tags), I'd be happy to show how to adapt your algorithm.

Happy holidays.

Depth first traversal can be accomplished with an array and unshift, breadth-first search via an array and push. Following pseudo-code converts to a flat list:

# -*- pseudo-mode -*-
traverse_queue = [ root ];
work_queue = [];

while ( work_queue is_not empty ) {
    node = shift( traverse_queue );

    push( work_queue, node ) if BFS;

    push/unshift( traverse_queue, children );

    push( work_queue, node ) if DFS;
}
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