There are a load of papers on the subject, I read a lot a couple of years ago. Some leading names: Fredkin, Margolus & Toffoli, Gerard Vichniac, Jarkko Kari, Te

There are a load of papers on the subject, I read a lot a couple of years ago. Some leading names: Fredkin, Margolus & Toffoli, Gerard Vichniac, Jarkko Kari, Tetsuya Hattori, Morita & Ueno, Shinji Takasue, mostly 70s and since. I made movies that looked like sunlight reflecting on ripples in a river (I mean, looked exactly) using 2D CA based on a couple of Rudy Rucker papers, based on (I believe) the original (1D) CA paper, analyzing non-linear effects on waves, modelled as a row of particles, neighbours joined with springs, sliding up and down frictionless rods. I used this super-simple formula to approximate the wave equation: a cell's height (each cell stores a number representing height of the water) = half the sum of the 4 neighbours from the previous generation, minus the cell's height in the gen before that. i.e. C_t=(Nsum_{t-1})/2-C_{t-2}. (Note that adding C_{t-2} to both sides produces a time-symmetric equation.) Amazing that it produced totally realistic-looking water! (I added a feature to show sunlight reflection if the 3D angle of the plane between each adjacent 4 points was in a particular small angle range) Different conserved quantities in CAs indeed correspond to different conserved quantities in the physics. (I don't remember the details enough now to say more.)