What's the impact of net-splits on block generation... over a long period of time?

Question

Part 1

For this question, assume the overall hashrate of the environment is constant.

• If 25% of the network hashpower were to be isolated (Australia had no Internet for example), what is the effect on block generation?

I suspect that blocks in Australia will take 75% longer to confirm, and the the main chain will confirm 75% faster (Edit: it will take 25% longer for the main chain to confirm, difficulty will adjust downward).

Part 2

If I extrapolate the effects suppose

1. This outage is long-lasting
2. A multiple of the 2016th block is reached on the main chain. Maybe several multiples.
3. Difficulty is adjusted.

Given that the Bitcoin client is hard coded to prevent a change in difficulty more than 4x the the current difficulty:

• What would happen to the isolated Australian chain if it reconnects to the main chain? (w.r.t. the difficulty adjustment)

• Suppose a different percent of the network were to become isolated. What combination of %isolated, duration, and network hashrate would cause a 4x difficulty to be reached?

Answer 1

If 25% of the network hashpower were to be isolated (Australia had no Internet for example), what is the effect on block generation?

Aussie transactions take 4x longer to confirm, actually. Everybody else's transactions take 33% longer (1.0/0.75)

What would happen to the isolated Australian chain if it reconnects to the main chain? (w.r.t. the difficulty adjustment)

It's instantly blown away, and the main chain is downloaded to all of the Aussie bitcoin clients.

Suppose a different percent of the network were to become isolated. What combination of %isolated, duration, and network hashrate would cause a 4x difficulty to be reached?

Suppose that 3/4 of miners suddenly have no internet access. For 8 weeks. That's when you'd see the difficulty drop to 1/4 of its previous value.