I am a senior student in UW, international, I majored in ACMS, it's not the discrete math branch, it's the the computational math branch.
When I tell people I majored in ACMS, most of them will just assume that I am in the discrete mathematic branch, the branch that is closest to computer science which is different from the computational math branch, therefore I felt the need to clarify.
Conway's game of life is cellular automation, slight perturbations in initial condition lead to completely different outcomes. It can have finite state oscillators, still life, and glider, which usually appear when it reaches equilibrium state. The above gif is a device call Slider Gun, and it's a very fascinating device in the game.
At first glance it might seems to be in O(MN) where M,N is the width and height of the grid of simulation, but I found a O(N) in-place algorithm with the help with internet and some thinking. The N represents the number of cells that are right next to a living cell or a living cell at each time frame.
People make Turing Machine in Conway's Game of Life.