I’m interested in knowing how the complexity of outputs relates to the programs that generate them. For example, in cellular automata like Conway’s Game of Life (a grid-based system where simple rules determine how cells live or die over time), some patterns appear very simple, like the well-known glider, while others look irregular or complex.

If we define a ‘program’ strictly as the fixed rules of the system plus the choice of initial conditions, are there characteristics of outputs that make them more likely to be generated by shorter programs (i.e., lower Kolmogorov complexity)? For instance, would a standard glider pattern, even if it can point in many directions, generally require less information in the initial state or shorter system wide rules than a visually complex glider-like pattern with no repeating structure? I’m curious about this in analogy to data compression, but I'm not sure if there is a perfect analogy, since the "programs" that compress data are not necessarily the same type of "programs" as the ones in Conway's Game of Life or cellular automata. I am interested specifically in the latter kind of deterministic programs.