Choose any three numbers. The differences between your numbers give you three new numbers. Repeat this operation to give a sequence.
In this example the sequence starts: $15, 39, 8 \to 24, 31, 7 \to 7, 24, 17 \to 17, 7, 10 ...$. What happens to this sequence. Investigate for different starting points. |

What do you notice? Can you explain what happens?

How about sequences starting with four numbers, or two numbers?

See the article Difference Dynamics Discussion.