Can every recursion be converted into iteration?

Question

A reddit thread brought up an apparently interesting question:

Tail recursive functions can trivially be converted into iterative functions. Other one

Answer 1

• Recursive function execution flow can be represented as a tree.

• The same logic can be done by a loop, which uses a data-structure to traverse that tree.

• Depth-first traversal can be done using a stack, breadth-first traversal can be done using a queue.

So, the answer is: yes. Why: https://stackoverflow.com/a/531721/2128327.

Can any recursion be done in a single loop? Yes, because

a Turing machine does everything it does by executing a single loop:

1. fetch an instruction,
2. evaluate it,
3. goto 1.