The key thing you end up needing is a clock (along with memory of course, yeah) I still remember clearly the day I in college read the SICP chapter on simulati

The key thing you end up needing is a clock (along with memory of course, yeah) I still remember clearly the day I in college read the SICP chapter on simulating circuits and realized how computers work -- a purely functional circuit combined with a clock to govern that circuit so its inputs come from memory which came from the previous state but its outputs go into memory for the next state. Prior to that I always had the same confusion you describe -- logic happens, but how does anything actually progress? Branching isn't really necessary per se in that you can do tricks to avoid it but essentially accomplish the same thing (differentiable computing leans heavily on this), eg if you want to select A or B, rather than saying `if(x) a else b`, you can say `xa + (1-x)b`