Put four numbers on the corners of a square. I’ll pick 1, 3, 14 and 39, in that order:

 1---

- 3
|    |
|    |
|    |
39---

-14

Between each pair, write their unsigned difference:

( 1)- 2-( 3)
|      |
38      11
|      |
(39)-15-(14)

Now you have a new square: (2, 11, 15, 38). I’m not going to keep drawing them; it’s a pain to typeset. But we repeat the process, getting differences of:

• (9,4,23,36)
• (5,19,13,27)
• (14,6,14,22)
• (8,8,8,8)
• (0,0,0,0) – and we’re done.

Including the first and last boxes, that took (fairly impressively) seven boxes to converge to zero.

There are all sorts of questions you can ask:

• Does every set of four integers eventually converge to zero?
• Can you come up with a set that takes eight boxes to converge? Ten? A hundred?
• What if you extend it to real numbers?

In fact, the tribonacci constant, $q \approx 1.839$, can be used to generate (effectively) the only Diffy box that doesn’t converge: (0, 1, $q(q-1)$, $q$). You may like to verify this!