Couldany universe satisfy the following conditions? (i) Each volume of space contains only a finite amount of information, because space and time come in discrete units. (ii) Over some range of size and speed, the mechanics of this world are approximately classical. Imagine a crystalline world of tiny, discrete “cells,” each knowing only what its nearest neighbors do. In such a universe, we’ll construct analogs of particles and fields, and ask what it would mean for these to satisfy constraints like conservation of momentum. In each case classical mechanics will break down—on scales both small and large—and strange phenomena will emerge: a maximal velocity, a slowing of internal clocks, a bound on simultaneous measurement, and quantumlike effects in very weak or intense fields.