I don't understand. How is its behavior not completely pre-determined, if it follows a static algorithm and the initial conditions are always the same?
If you want the mind-blowing read on this, it is pre-determined, and contains very little information content; only the specification of the field, the rules, the initial state (often very compressible since it's one point), and the number of iterations it runs for. Add a dash of information for the coloration if you want to specify the image rather than the raw state.
And that's how quickly "low-information states" become very superficially-rich-seeming states. You'd think all the things you can represent with just a handful of bits would all be relatively boring or regular things, but this disproves that.
I often find myself boggling at just how little math it takes for our brains to be essentially completely incapable of handling it. If you gave a human who had never seen this before all the information above and asked them to guess what it would do, the odds of them being right are basically zero. And this hardly even wading in to the shallow end of the world of math and where we can get with more bits.
There's some ways we pride ourselves on how good at math we are, and there's some truth in that. But in other ways, we cognitively fall down and go splat on even the simplest systems.
Speaking of the richness of low-information states... there's also a kind of opposite to this: a lack of richness of high-information states. Consider a beam of light entering a liquid like water. There's a great deal of noise and variation in the positions of the water molecules, but due to the low-dimension (3) of the space and the high density of the material, there is an inevitable kind of 'regularity' that makes the material act on aggregate as though it were simply a region of simple refraction, rather than a complex superposition of billions of electromagnetic interactions.
Actually, this is probably captured by the idea of randomness.
It is predetermined. Just the same way Conway's Game of Life is predetermined. The interesting thing is when you have multiple of them or different beginning board states.
