It may be related to statistical mechanics, with the concepts of microstates, macrostates and entropy. In your first example there are 2 microstates per macrostate, so the entropy of the system, as far as your friend is concerned, is log 2 = 1. In your second example there are say, 2^20 pixels 2^5 bit each, and if there are, say, 2^13 different possible distinct pictures that can still be reasonably called “Lion on grass” (a macrostate), then the entropy of “Lion on grass” is 2^22.
It may be related to statistical mechanics, with the concepts of microstates, macrostates and entropy. In your first example there are 2 microstates per macrostate, so the entropy of the system, as far as your friend is concerned, is log 2 = 1. In your second example there are say, 2^20 pixels 2^5 bit each, and if there are, say, 2^13 different possible distinct pictures that can still be reasonably called “Lion on grass” (a macrostate), then the entropy of “Lion on grass” is 2^22.