You've obfuscated nicely!

The single pixel case only demonstrates that you need one extra pixel in each dimension, not twice as many.

If you have a 100 by 100 normal map, exactly the same information is found in a 101 by 101 bump or displacement map.

By analogy, I can describe a bank account as a series of balances, or as a series of transactions (deltas). Given one I can produce the other. The amount of data is the same.

Consider this bank account.

Initial balance 0

File 1: Subsequence balances - 10, 30, 50, 45, 70

File 2: Transactions - 10, 20, 20, -5, 25

 

Is there any difference in the information? How about the information density? No to both. But if you ask me to list the transactions, File 2 has them directly, while in File 1 I need a pair of balances to calculate a transaction - information that is directly stored in File 2, but readily reproduced from the data in File 1. There is a difference in efficiency, but not density.

The same is roughly true of normal versus bump map. The bump is in File 1 format - actual balances. The normal is (sort of) in File 2 format - deltas (or slopes).

 

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Renderosity forum reply notifications are wonky. If I read a follow-up in a thread, but I don't myself reply, then notifications no longer happen AT ALL on that thread. So if I seem to be ignoring a question, that's why. (Updated September 23, 2019)