Cool and everything, but not sure about the relation to Kolmogorov complexity. 1) Are there any assumptions about the compression algorithm that approximates K

Cool and everything, but not sure about the relation to Kolmogorov complexity. 1) Are there any assumptions about the compression algorithm that approximates KC? E.g., I can imagine a compression algorithm which stops as soon as it manages to compress data by a single byte, and I don't think that approximates KC. 2) Isn't the KC of all these cellular automata basically the same, and rather low? It's always just Life with different constants, right? (Sometimes a bit lower, when the constants allow for further compression.) Edit: I see the mistake now, the CA needs to include initial conditions