Circle of Differences

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Grade Vs Difficulty:
  EasyModerateChallengingPerplexing
1-2
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5-6
7-8
9-10
11-12
13-14

Place numbers at the vertices of a regular polygon. A square makes a good beginning. Then at the midpoint of each side, place the difference of the adjacent numbers, creating a new polygon. Repeat. Does it eventually become boring? What sets of numbers last the longest before becoming boring?