Conway's Game of Life to expand QR code

Question

If you use a QR code as a seed for Conway's Game of Life, and have information for

A) How many steps you should run it for, and

B) The size of the new square (where to put the border after you are done running)

Would the information be compressed? There could be a larger QR code (if you pick the right base value), and a larger QR code (I think?) means more information. Also, would there be a limit to the possible compression?

Answer 1

Compression is often relative: using $n$ bits of information, you cannot represent more than $2^n$ different informations.

So, sure, using an $n\times n$ QR-code as a seed to encode an $N\times N$ bigger QR-code, the way you describe, could be a way to compress some information, but:

• can it compress any $N\times N$ QR-code? (answer: no)
• given a $N\times N$ QR-code, is it easy to find a corresponding $n\times n$ seed? (answer: I don't think so)

As for the limit for compression, in a way, there is none. For example, you can decide that the word "blublu" encode the value of the busy beaver for the googolplex. This is a very good compression ratio. The problem is this is a good compression ratio for THIS information, and not general information.